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On k-intersection edge colourings
Discussiones Mathematicae Graph Theory, 2009 We propose the following problem. For some \(k\geq 1\), a graph \(G\) is to be properly edge coloured such that any two adjacent vertices share at most \(k\) colours. We call this the \(k\)-intersection edge colouring. The minimum number of colours sufficient to guarantee such a colouring is the \(k\)-intersection chromatic index and is denoted ...
Rahul Muthu +2 more
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Applications of Edge Colouring of Fuzzy Graphs [PDF]
Informatica, 2020 Summary: Colouring of graphs is being used in several representations of real world systems like map colouring, traffic signalling, etc. This study introduces the edge colouring of fuzzy graphs. The chromatic index and the strong chromatic index are defined and related properties are investigated.
Rupkumar Mahapatra +2 more
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Line game-perfect graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceThe $[X,Y]$-edge colouring game is played with a set of $k$ colours on a graph $G$ with initially uncoloured edges by two players, Alice (A) and Bob (B). The players move alternately. Player $X\in\{A,B\}$ has the first move. $Y\in\{A,B,-\}$.
Stephan Dominique Andres, Wai Lam Fong
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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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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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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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Ars Mathematica Contemporanea, 2011 A facial parity edge colouring of a connected bridgeless plane graph is an edge colouring in which no two face-adjacent edges (consecutive edges of a facial walk of some face) receive the same colour, in addition, for each face α and each colour c, either no edge or an odd number of edges incident with α is coloured with c.
Czap, Július +2 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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Distinguishing graphs by edge-colourings
European Journal of Combinatorics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rafal Kalinowski, Monika Pilsniak
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