Results 21 to 30 of about 2,800 (262)
GRACEFUL CHROMATIC NUMBER OF SOME CARTESIAN PRODUCT GRAPHS
Ural Mathematical Journal, 2023 A graph \(G(V,E)\) is a system consisting of a finite non empty set of vertices \(V(G)\) and a set of edges \(E(G)\). A (proper) vertex colouring of \(G\) is a function \(f:V(G)\rightarrow \{1,2,\ldots,k\},\) for some positive integer \(k\) such that ...
I Nengah Suparta +3 more
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A note on the size Ramsey numbers for matchings versus cycles [PDF]
Mathematica Bohemica, 2021 For graphs $G$, $F_1$, $F_2$, we write $G \rightarrow(F_1, F_2)$ if for every red-blue colouring of the edge set of $G$ we have a red copy of $F_1$ or a blue copy of $F_2$ in $G$.
Edy Tri Baskoro, Tomáš Vetrík
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Tutte's Edge-Colouring Conjecture
Journal of Combinatorial Theory, Series B, 1997 In 1966 Tutte conjectured that every 2-connected cubic graph not containing the Petersen graph as a minor is 3-edge-colourable. The conjecture is still open, but it is shown in this paper that it is true in general, provided that it is true for two special kinds of cubic graphs that are almost planar.
Neil Robertson 0001 +2 more
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Complexity of greedy edge-colouring [PDF]
Journal of the Brazilian Computer Society, 2015 The Grundy index of a graph G = (V, E) is the greatest number of colours that the greedy edge-colouring algorithm can use on G. We prove that the problem of determining the Grundy index of a graph G = (V, E) is NP-hard for general graphs. We also show that this problem is polynomial-time solvable for caterpillars.
Havet, Frédéric +2 more
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On Fibonacci numbers in edge coloured trees [PDF]
Opuscula Mathematica, 2017 In this paper we show the applications of the Fibonacci numbers in edge coloured trees. We determine the second smallest number of all \((A,2B)\)-edge colourings in trees. We characterize the minimum tree achieving this second smallest value.
Urszula Bednarz +4 more
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An Even 2-Factor in the Line Graph of a Cubic Graph
Theory and Applications of Graphs, 2022 An even 2-factor is one such that each cycle is of even length. A 4- regular graph G is 4-edge-colorable if and only if G has two edge-disjoint even 2- factors whose union contains all edges in G.
SeungJae Eom, Kenta Ozeki
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Colour at edges and colour spreading in McCollough effects
Vision Research, 1999 Broerse and O'Shea [(1995) Vision Research, 35, 207-226] proposed that the subjective colours in McCollough effects (MEs) consist of two components: edge colours appearing along the edges of contours, and spread colours radiating from edge colours into adjacent uncontoured regions of test patterns. This proposal was examined in five experiments. First,
Broerse, Jack +2 more
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A rainbow blow-up lemma for almost optimally bounded edge-colourings
Forum of Mathematics, Sigma, 2020 A subgraph of an edge-coloured graph is called rainbow if all its edges have different colours. We prove a rainbow version of the blow-up lemma of Komlós, Sárközy, and Szemerédi that applies to almost optimally bounded colourings.
Stefan Ehard, Stefan Glock, Felix Joos
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(1, 2)-rainbow connection number at most 3 in connected dense graphs
Electronic Journal of Graph Theory and Applications, 2023 Let G be an edge-coloured connected graph G. A path P in the graph G is called l-rainbow path if each subpath of length at most l + 1 is rainbow. The graph G is called (k, l)-rainbow connected if any two vertices in G are connected by at least k pairwise
Trung Duy Doan, Le Thi Duyen
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Aspects of edge list-colourings
Discrete Mathematics, 2001 An assignment of colours to the edges of a multigraph is called an \(s\)-improper edge-colouring if no colour appears on more than \(s\) edges incident with any given vertex. In this paper it is proved that if \(L:E(G) \rightarrow 2^{N}\) is an assignment of lists of colours to the edges of a multigraph \(G\) with \(|L(e)|\geq \lceil \max {d(u),d(v)}/s\
Anthony J. W. Hilton +2 more
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