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Title Journal of graph theory Issue data Hoboken : John Wiley & Sons , 1996 ISSN 0364-9024 (print)1097-0118 (online) Form. Descr. časopisy - journals, elektronické časopisy - electronic journals Year, No. Vol. 22 no. 3 (1996) Language English Country United States of America URL Link na zdrojový dokument Link na zdrojový dokument Public work category GII Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References - PERIODIKÁ - Súborný záznam periodika (1) - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika ARTICLES 1996: Decompositions and reductions of snarks 
journal
Title Decompositions and reductions of snarks Author info R. Nedela, M. Skoviera Author Nedela Roman 1960- (50%) UMBFP12 - Inštitút matematiky a informatiky
Co-authors Škoviera Martin (50%)
Source document Journal of graph theory. Vol. 22, no. 3 (1996), pp. 253-279. - Hoboken : John Wiley & Sons, 1996 Keywords matematika - mathematics grafy - charts - graphs Language English Country Slovak Republic systematics 51 Annotation According to M. Gardner [''Mathematical Games: Snarks, Boojums, and Other Conjectures Related to the Four-Color-Map Theorem,'' Scientific American, vol. 234 (1976), pp. 126-130], a snark is a nontrivial cubic graph whose edges cannot be properly colored by three colors. The problem of what ''nontrivial'' means is implicitly or explicitly present in most papers on snarks, and is the main motivation of the present paper. Our approach to the discussion is based on the following observation. If G is a snark with a k-edge-cut producing components G(1) and G(2), then either one of G(1) and G(2) is not 3-edge-colorable, or by adding a ''small'' number of vertices to either component one can obtain snarks <(G)over tilde (1)> and <(G)over tilde (2)> whose order does not exceed that of G. The two situations lead to a definition of a L-reduction and k-decomposition of G. Snarks that for m < k do not admit m-reductions, m-decompositions, or both are k-irreducible, k-indecomposable, and k-simple, rAccording to M. Gardner [''Mathematical Games: Snarks, Boojums, and Other Conjectures Related to the Four-Color-Map Theorem,'' Scientific American, vol. 234 (1976), pp. 126-130], a snark is a nontrivial cubic graph whose edges cannot be properly colored by three colors. The problem of what ''nontrivial'' means is implicitly or explicitly present in most papers on snarks, and is the main motivation of the present paper. Our approach to the discussion is based on the following observation. If G is a snark with a k-edge-cut producing components G(1) and G(2), then either one of G(1) and G(2) is not 3-edge-colorable, or by adding a ''small'' number of vertices to either component one can obtain snarks <(G)over tilde (1)> and <(G)over tilde (2)> whose order does not exceed that of G. The two situations lead to a definition of a L-reduction and k-decomposition of G. [...] Public work category ADE No. of Archival Copy 28530 Repercussion category BRINKMANN, Gunnar - GOEDGEBEUR, Jan - HAGGLUND, Jonas - MARKSTROM, Klas. Generation and properties of snarks. In Journal of combinatorial theory series B. ISSN 0095-8956, 2013, vol. 103, no. 4, pp. 468-488.
MACAJ, Martin - MAZAK, Jan. Asymptotic lower bounds on circular chromatic index of snarks. In Electronic journal of combinatorics [online]. 2013, vol. 20, no. 2, [cit. 2014-02-28]. ISSN 1077-8926. Dostupné na: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i2p2
KUTNAR, Klavdija - MARUSIC, Dragan - NAIMZADA, A. K. et al. Some Topics in Graph Theory. In Networks, topology and dynamics : theory and applications to economics and social systems. Berlin : Springer Verlag, 2009. ISBN 978-3-540-68407-7, pp. 3-22.
BROERSMA, Hajo - FIJAVZ, Gasper - KAISER, Tomas et al. Contractible subgraphs, Thomassen´s conjecture and the dominating cycle conjecture for snarks. In Discrete mathematics. ISSN 0012-365X, 2008, vol. 308, no. 24, pp. 6064-6077.
PATAKFALVI, Zsolt. Line-graphs of cubic graphs are normal. In Discrete mathematics. ISSN 0012-365X, 2008, vol. 308, no. 12, pp. 2351-2365.
MADARAS, Tomas - SOTAK, Roman. More maps of p-gons with a ring of q-gons. In Ars combinatoria. ISSN 0381-7032, 2007, vol. 85, pp. 395-403.
BRADLEY, R.C. On the number of colorings of a snark minus an edge. In Journal of graph theory. ISSN 0364-9024, 2006, vol. 51, no. 3, pp. 251-259.
MYNHARDT, C.M. - BURGER, A.P. - CLARK, T.C. et al. Altitude of regular graphs with girth at least five. In Discrete mathematics. ISSN 0012-365X, 2005, vol. 294, no. 3, pp. 241-257.
POTOCNIK, P. Edge-colourings of cubic graphs admitting a solvable vertex-transitive group of automorphisms. In Journal of combinatorial theory series B. ISSN 0095-8956, 2004, vol. 91, no. 2, pp. 289-300.
DVORAK, Z. - KARA, J. - KRAL, D. et al. An algorithm for cyclic edge connectivity of cubic graphs. In Algorithm theory - SWAT 2004. Berlin : Springer Verlag, 2004. ISBN 3-540-22339-8, pp. 236-247.
CAVICCHIOLI, A. - MURGOLO, T.E. - RUINI, B. - SPAGGIARI, F. Special classes of snarks. In Acta applicandae mathematicae. ISSN 0167-8019, 2003, vol. 76, no. 1, pp. 57-88.
STEFFEN, E. Non-bicritical critical snarks. In Graphs and combinatorics. ISSN 0911-0119, 1999, vol. 15, no. 4, pp. 473-480.
BRINKMANN, G. - STEFFEN, E. Snarks and reducibility. In Ars combinatoria. ISSN 0381-7032, 1998, vol. 50, pp. 292-296.
STEFFEN, E. Classifications and characterizations of snarks. In Discrete mathematics. ISSN 0012-365X, 1998, vol. 188, no. 1-3, pp. 183-203.
CAVICCHIOLI, A. - MESCHIARI, M. - RUINI, B. - SPAGGIARI, F. A survey on snarks and new results : products, reducibility and a computer search. In Journal of graph theory. ISSN 0364-9024, 1998, vol. 28, no. 2, pp. 57-86.
BROERSMA, H. - FIJAVŽ, G. - KAISER, T. et al. Contractible Subgraphs, Thomassen's Conjecture and the Dominating Cycle Conjecture for Snarks. In Electronic Notes in Discrete Mathematics [online]. 2007, vol. 28, pp. 55-59 [cit. 2014-02-28]. ISSN 1571-0653. Dostupné na: http://www.sciencedirect.com/science/article/pii/S0012365X07009387.
FIOL, M.A. - VILALTELLA, J. Some results on the structure of multipoles in the study of snarks. In Electronic journal of combinatorics [online]. 2015, vol. 22, no. 1, article no. P1.45 [cit. 2015-04-27]. ISSN 1077-8926. Dostupné na: http://arxiv.org/pdf/1308.0480v1.pdf
STEFFEN, Eckhard. On bicritical snarks. In Mathematica slovaca. ISSN 0139-9918, 2001, vol. 51, no. 2, pp. 141-150.
GRÜNEWALD, Stefan - STEFFEN, Eckhard. Cyclically 5-edge connected non-bicritical critical snarks. In Discussiones mathematicae graph theory. ISSN 1234-3099, 1999, vol. 19, no. 1, pp. 5-11.
HRNČIAR, Pavel. On color-closed multipoles. In Acta Universitatis Matthiae Belii : series mathematics, vol. 7. Banská Bystrica : Univerzita Mateja Bela, 1999. ISBN 80-8055-347-5, pp. 31-34.
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Title Which generalized Petersen graphs are Cayley graphs? Author info Roman Nedela, Martin Škoviera Title Subtitle Translation : Ktoré zovšeobecnené Petersenove grafy sú Cayleyho grafmi? Author Nedela Roman 1960- (50%) UMBFP12 - Inštitút matematiky a informatiky
Co-authors Škoviera Martin (50%)
Source document Journal of graph theory. Vol. 19, no. 1 (1995), pp. 1-11. - Hoboken : John Wiley & Sons, 1995 Keywords grafy - charts - graphs grupy štúdie Language English Country United States of America systematics 519.1 Public work category ADE Repercussion category ZHOU, Jin-Xin - FENG, Yan-Quan. Cubic bi-Cayley graphs over abelian groups. In European journal of combinatorics. ISSN 0195-6698, 2014, vol. 36, pp. 679-693.
EXOO, Geoffrey - JAJCAY, Robert - SIRAN, Jozef. Cayley cages. In Journal of algebraic combinatorics. ISSN 0925-9899, 2013, vol. 38, no. 1, pp. 209-224.
HORVAT, Boris - PISANSKI, Tomaz - ZITNIK, Arjana. Isomorphism checking of I-graphs. In Graphs and combinatorics. ISSN 0911-0119, 2012, vol. 28, no. 6, pp. 823-830.
ZITNIK, Arjana - HORVAT, Boris - PISANSKI, Tomaz. All generalized Petersen graphs are unit-distance graphs. In Journal of the Korean Mathematical Society. ISSN 0304-9914, 2012, vol. 49, no. 3, pp. 475-491.
ZHOU, Jin Xin - FENG, Yan Quan. Regular maps of graphs of order 4p. In Acta mathematica sinica. ISSN 1439-8516, 2012, vol. 28, no. 5, pp. 989-1012.
ZHOU, Jin-Xin - FANG, Yan-Quan. Cubic vertex-transitive non-Cayley graphs of order 8p. In Electronic journal of combinatorics [online]. 2012, vol. 19, no. 1, article no. 53 [2014-03-06]. ISSN 1077-8926. Dostupné na: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i1p53/pdf
KUTNAR, Klavdija - MARUSIC, Dragan - ZHANG, Cui. On cubic non-Cayley vertex-transitive graphs. In Journal of graph theorz. ISSN 0364-9024, 2012, vol. 69, no. 1, pp. 77-95.
LI, Feng - WANG, Wei - XU, Zongben - ZHAO, Haixing. Some results on the lexicographic product of vertex-transitive graphs. In Applied mathematics letters. ISSN 0893-9659, 2011, vol. 24, no. 11, pp. 1924-1926.
ZHOU, Jin-Xin - FENG, Yan-Quan. Cubic vertex-transitive graphs of order 2pq. In Journal of graph theory. ISSN 0364-9024, 2010, vol. 65, no. 4, pp. 285-302.
MWAMBENE, Eric. Cayley graphs on left quasi-groups and groupoids representing k-generalised Petersen graphs. In Discrete mathematics. ISSN 0012-365X, 2009, vol. 309, no. 8, pp. 2544-2547.
KUTNAR, Klavdija - MARUSIC, Dragan. A complete classification of cubic symmetric graphs of girth 6. In Journal of combinatorial theory series B. ISSN 0095-8956, 2009, vol. 99, no. 1, pp. 162-184.
WILSON, Steve. Unexpected symmetries in unstable graphs. In Journal of combinatorial theory series B. ISSN 0095-8956, 2008, vol. 98, no. 2, pp. 359-383.
FENG, Yan-Quan - KWAK, Jin Ho. Cubic symmetric graphs of order a small number times a prime or a prime square. In Journal of combinatorial theory series B. ISSN 0095-8956, 2007, vol. 97, no. 4, pp. 627-646.
JAJCAY, Robert - MALNIC, Aleksander - MARUSIC, Dragan. On the number of closed walks in vertex-transitive graphs. In Discrete mathematics. ISSN 0012-365X, 2007, vol. 307, no. 3-5, pp. 484-493.
SARAZIN, Marko Lovrecic - PACCO, Walter - PREVITALI, Andrea. Generalizing the generalized Petersen graphs. In Discrete mathematics. ISSN 0012-365X, 2007, vol. 307, no. 3-5, pp. 534-543.
POTOCNIK, Primoz - SAJNA, Mateja - VERRET, Gabriel. Mobility of vertex-transitive graphs. In Discrete mathematics. ISSN 0012-365X, 2007, vol. 307, no. 3-5, pp. 579-591.
KWAK, J.H. - KWON, Y.S. Regular orientable embeddings of complete bipartite graphs. In Journal of graph theory. ISSN 0364-9024, 2005, vol. 50, no. 2, pp. 105-122.
FENG, Y.Q. On vertex-transitive graphs of odd prime-power order. In Discrete mathematics. ISSN 0012-365X, 2002, vol. 248, no. 1-3, pp. 265-269.
MALNIC, A. Action graphs and coverings. In Discrete mathematics. ISSN 0012-365X, 2002, vol. 244, no. 1-3, pp. 299-322.
ALSPACH, B. - QIN, Y. S. Hamilton-connected Cayley graphs on Hamiltonian groups. In European journal of combinatorics. ISSN 0195-6698, 2001, vol. 22, no. 6, pp. 777-787.
BACA, M. Consecutive-magic labeling of generalized Petersen graphs. In Utilitas mathematica. ISSN 0315-3681, 2000, vol. 58, pp. 237-241.
SARAZIN, M.L. A note on the generalized Petersen graphs that are also Cayley graphs. In Journal of combinatorial theory series B. ISSN 0095-8956, 1997, vol. 69, no. 2, pp. 226-229.
CONDER, Marston D.E. - PISANSKI, Tomasz - ZITNIK, Arjana. GI-graphs : a new class of graphs with many symmetries. In Journal of algebraic combinatorics. ISSN 0925-9899, 2014, vol. 40, no. 1, pp. 209-231.
JENDROĽ, Stanislav - ŽOLDÁK, Vladimír. The irregularity strength of generalized Petersen graphs. In Mathematica Slovaca. ISSN 1337-2211, 1995, vol. 45, no. 2, pp. 107-113.
JAJCAY, Robert - ŠIRÁŇ, Jozef. More constructions of vertex-transitive non-Cayley graphs based on counting closed walks. In Australasian journal of combinatorics. ISSN 1034-4942, 1996, vol. 14, pp. 121-132.
SCAPELLATO, Raffaele. Vertex-transitive graphs and digraphs. In Graph symmetry : algebraic methods and applications. [Houten] : Springer Netherlands, 1997. ISBN 978-90-481-4885-1, pp. 319-378.
MARUŠIČ, Dragan - PISANSKI, Tomaž. The remarkable generalized Petersen graphs G(8, 3). In Mathematica Slovaca. ISSN 1337-2211, 2000, vol. 50, no. 2, pp. 117-121.
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Title Journal of graph theory Issue data Hoboken : John Wiley & Sons , 1995 ISSN 0364-9024 (print)1097-0118 (online) Form. Descr. časopisy - journals, elektronické časopisy - electronic journals Year, No. Vol. 19 no. 1 (1995) Language English Country United States of America URL Link na zdrojový dokument Link na zdrojový dokument Public work category GII Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References - PERIODIKÁ - Súborný záznam periodika (1) - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika ARTICLES 1995: Which generalized Petersen graphs are Cayley graphs? journal
Title Journal of graph theory Issue data Hoboken : John Wiley & Sons , 1994 ISSN 0364-9024 (print)1097-0118 (online) Form. Descr. časopisy - journals, elektronické časopisy - electronic journals Year, No. Vol. 18 no. 1 (1994) Language English Country United States of America URL Link na zdrojový dokument Link na zdrojový dokument Public work category GII Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References - PERIODIKÁ - Súborný záznam periodika (1) - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika ARTICLES 1994: Minimal locally cyclic triangulations of the projective plane journal
Title Minimal locally cyclic triangulations of the projective plane Author info Steve Fisk, Bojan Mohar, Roman Nedela Title Subtitle Translation : Minimálne lokálne cyklické triangulácie projektívnej roviny Author Fisk Steve (34%)
Co-authors Mohar Bojan (33%)
Nedela Roman 1960- (33%) UMBFP12 - Inštitút matematiky a informatiky
Source document Journal of graph theory. Vol. 18, no. 1 (1994), pp. 25-35. - Hoboken : John Wiley & Sons, 1994 Keywords matematika - mathematics topológia - topology grafy - charts - graphs triangulácie - triangulation projektívna rovina kontrakcia štúdie Language English Country United States of America systematics 515.1 Public work category ADE Repercussion category LIEBERS, Annegret. Planarizing graphs - a survey and annotated bibliography. In Journal of graph algorithms and applications. ISSN 1526-1917, 2001, vol. 5, no. 1, pp. 1-74.
GROSS, Jonathan L. - TUCKER, Thomas W. Topological graph theory. [Mineola] : Dover Publications, 2001. 384 p. ISBN 0486417417.
NEGAMI, S. Triangulations. In GROSS, Jonathan L. - YELLEN, Jay - ZHANG, Ping. Handbook of graph theory. 2nd ed. [Boca Raton] : CRC Press, 2013. ISBN 1439880182, pp. [737-760].
Catal.org. UKUMB###BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika book