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Title Perfect-matching covers of cubic graphs with colouring defect 3 Author info Ján Karabáš ... [et al.] Author Karabáš Ján 1977- (25%) UMBFP05 - Katedra informatiky
Co-authors Máčajová Edita (25%)
Nedela Roman 1960- (25%)
Another authors Škoviera Martin (Author) (25%)
Source document Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications : EUROCOMB’23. Pp. 639-646. - Brno : Masarykova univerzita v Brně, 2023 ; European Conference on Combinatorics, Graph Theory and Applications medzinárodná konferencia Keywords grafy - charts - graphs kubické grafy - cubic charts teória grafov - graph theory Form. Descr. príspevky v zborníku - proceedings papers Language English Country Czech Republic URL Link na plný text Public work category AFC No. of Archival Copy 53352 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ 
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Title Berge covers of cubic graphs with colouring defect 3 Author info Martin Škoviera ... [et al.] Author Škoviera Martin (25%)
Co-authors Karabáš Ján 1977- (25%) UMBFP05 - Katedra informatiky
Máčajová Edita (25%)
Nedela Roman 1960- (25%)
Source document BGTC 2023 : Belgian graph theory conference on structure and algorithms. Pp. 16. - Belgicko : Ghent University, 2023 ; Belgian Graph Theory Conference on Structure and Algorithms konferencia Keywords kubické grafy - cubic charts grafy - charts - graphs teória grafov - graph theory Form. Descr. abstrakty - abstracts Language English Country Belgium Public work category GII No. of Archival Copy 53509 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ article
Title Girth, oddness, and colouring defect of snarks Author info Ján Karabáš, Edita Máčajová ... [et al.] Author Karabáš Ján 1977- (25%) UMBFP05 - Katedra informatiky
Co-authors Máčajová Edita (25%)
Nedela Roman 1960- (25%)
Škoviera Martin (25%)
Source document Discrete Mathematics. Vol. 345, no. 11 (2022), pp. [1-10]. - Amsterdam : Elsevier B.V., 2022 Keywords snark grafy - charts - graphs Form. Descr. články - journal articles Language English Country Netherlands URL Link na plný text Public work category ADM No. of Archival Copy 52279 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika article
Title Perfect matching index of cubic graphs with defect 3 Author info Ján Karabáš ... [et al.] Author Karabáš Ján 1977- (25%)
Co-authors Máčajová Edita (25%)
Nedela Roman 1960- (25%)
Škoviera Martin (25%)
Source document Booklet of abstracts for the 56th Czech-Slovak Conference on Graph Theory. Pp. 37. - Bratislava : Slovenská technická univerzita, 2021 ; Czech and Slovak Conference on Graph Theory 2021 konferencia Keywords grafy - charts - graphs kubické grafy - cubic charts Form. Descr. abstrakty - abstracts Language English Country Slovak Republic URL Link na zdrojový dokument Public work category AFH No. of Archival Copy 12483 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ article
Title Cubic graphs of defect 3 Author info Ján Karabáš ... [et al.] Author Karabáš Ján 1977- (25%)
Co-authors Máčajová Edita (25%)
Nedela Roman 1960- (25%)
Škoviera Martin (25%)
Source document Booklet of abstracts for the 56th Czech-Slovak Conference on Graph Theory. Pp. 38. - Bratislava : Slovenská technická univerzita, 2021 ; Czech and Slovak Conference on Graph Theory 2021 konferencia Keywords grafy - charts - graphs kubické grafy - cubic charts Form. Descr. abstrakty - abstracts Language English Country Slovak Republic URL Link na zdrojový dokument Public work category AFH No. of Archival Copy 12543 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ article
Title Girth, oddness, and colouring defect of snarks Author info Ján Karabáš ... [et al.] Author Karabáš Ján 1977- (25%)
Co-authors Máčajová Edita (25%)
Nedela Roman 1960- (25%)
Škoviera Martin (25%)
Source document Booklet of abstracts for the 56th Czech-Slovak Conference on Graph Theory. Pp. 32. - Bratislava : Slovenská technická univerzita, 2021 ; Czech and Slovak Conference on Graph Theory 2021 konferencia Keywords voľne žijúce živočíchy - wild animals hady sfarbenie živočíchov Form. Descr. abstrakty - abstracts Language English Country Slovak Republic URL Link na zdrojový dokument Public work category AFH No. of Archival Copy 12477 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ article
Title 6-decomposition of snarks Author info Ján Karabáš, Edita Máčajová, Roman Nedela Author Karabáš Ján 1977- (34%) UMBFP12 - Inštitút matematiky a informatiky
Co-authors Máčajová Edita (33%)
Nedela Roman 1960- (33%) UMBFP10 - Katedra matematiky
Source document European Journal of Combinatorics. Vol. 34, no. 1 (2013), pp. 111-122. - London : Academic Press, 2013 Keywords matematika - mathematics snark 6-decomposition Language English systematics 51 Annotation A snark is a cubic graph with no proper $3$-edge-colouring. In 1996, Nedela and /v Skoviera proved the following theorem: Let G be a snark with an k-edge-cut, k>= 2, whose removal leaves two 3-edge-colourable components M and N. Then both M and N can be completed to two snarks $/tilde M$ and $/tilde N$ of order not exceeding that of G by adding at most $/kappa(k)$ vertices, where the number $/kappa(k)$ only depends on $k$. The known values of the function $/kappa(k)$ are $/kappa(2)=0$, $/kappa(3)=1$, $/kappa(4)=2$ (Goldberg, 1981), and $/kappa(5)=5$ (Cameron, Chetwynd, Watkins, 1987). The value $/kappa(6)$ is not known and is apparently difficult to calculate. In 1979, Jaeger conjectured that there are no 7-cyclically-connected snarks. If this conjecture holds true, then $/kappa(6)$ is the last important value to determine. The paper is aimed attacking the problem of determining $/kappa(6)$ by investigating the structure and colour properties of potential complements in $6$-decompositions of snarks. We find a set of $14$ complements that suffice to perform $6$-decompositions of snarks with at most $30$ vertices. We show that if this set is not complete to perform $6$-decompositions of all snarks, then $/kappa(6)/geq 20$ and there are strong restrictions on the structure of (possibly) missing complements. Public work category AFC No. of Archival Copy 25350 Repercussion category FIOL, M.A. - MAZZUOCCOLO, G. - STEFFEN, E. On measures of edge-uncolorability of cubic graphs : a brief survey and some new results. In arXiv:1702.07156 [math.CO] [online]. New York : Cornell Univerisity Library, 2017, [1-39][cit. 2018-22-02]. Dostupné na: https://arxiv.org/pdf/1702.07156.pdf
FIOL, M. A. - VILALTELLA, J. Some results on the structure of multipoles in the study of snarks. In Electronic journal of combinatorics. ISSN 1077-8926, 2015, vol. 22, no. 1.
FIOL, M. A. - MAZZUOCCOLO, G. - STEFFEN, E. Measures of edge-uncolorability of cubic graphs. In Electronic journal of combinatorics. ISSN 1077-8926, 2018, vol. 25, no. 4.
OZEKI, Kenta. Kempe equivalence classes of cubic graphs embedded on the projective plane. In Combinatorica. ISSN 0209-9683, 2022, vol. 42, no. 2, pp. 1451-1480.
MAZAK, Jan - RAJNIK, Jozef - SKOVIERA, Martin. Morphology of small snarks. In Electronic journal of combinatorics. ISSN 1077-8926, 2022, vol. 29, no. 4, pp. 1-46.
SKRINAROVA, Jarmila - DUDAS, Adam. Optimization of the functional decomposition of parallel and distributed computations in graph coloring with the use of high-performance computing. In IEEE access. ISSN 2169-3536, 2022, vol. 10, pp. 34996-35011.
DUDÁŠ, Adam - ŠKRINÁROVÁ, Jarmila - KISS, Adam. On graph coloring analysis through visualization. In Information and digital technologies 2021 : proceedings of the international conference, Žilina, 22.-24.06.2021. 1. vyd. Danvers : Institute of electrical and electronics engineers, 2021. ISBN 978-1-6654-3692-2, pp. 71-78.
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