Results 41 to 50 of about 10,769 (289)
On critical graphs with chromatic index 4 [PDF]
, 1974 It is shown that the number of vertices of valency 2 in a critical graph with chromatic index 4 is at most 1/3 of the total number of vertices, and that there exist critical graphs with just one vertex of valency 2, but none with exactly two vertices of ...
Jakobsen, Ivan Tafteberg +1 more
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The chromatic index of multigraphs of order at most 10 [PDF]
, 1997 The maximum of the maximum degree and the “odd set quotients” provides a well-known lower bound φ(G) for the chromatic index of a multigraph G. Plantholt proved that if G is a multigraph of order at most 8, its chromatic index equals φ(G) and that if G ...
Plantholt, Michael J. +3 more
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Twin edge colorings of certain square graphs and product graphs
Electronic Journal of Graph Theory and Applications, 2016 A twin edge $k\!$-coloring of a graph $G$ is a proper edge $k$-coloring of $G$ with the elements of $\mathbb{Z}_k$ so that the induced vertex $k$-coloring, in which the color of a vertex $v$ in $G$ is the sum in $\mathbb{Z}_k$ of the colors of the edges ...
R Rajarajachozhan, R. Sampathkumar
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AVD proper edge-coloring of some families of graphs
International Journal of Mathematics for Industry, 2021 Adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for the proper edge-coloring of [Formula: see text] in which no two adjacent vertices are incident to edges colored with the same set of colors.
J. Naveen
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The Distance-t Chromatic Index of Graphs [PDF]
Combinatorics, Probability and Computing, 2013 We consider two graph colouring problems in which edges at distance at most t are given distinct colours, for some fixed positive integer t. We obtain two upper bounds for the distance-t chromatic index, the least number of colours necessary for such a colouring. One is a bound of (2-ε)Δt for graphs of maximum degree at most Δ, where ε is some absolute
Tomás Kaiser, Ross J. Kang
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On the chromatic index of outerplanar graphs [PDF]
, 1975 Vizing [Diskret. Analiz 3 (1964), 25–30] has shown that if ϱ denotes the maximum valency of a simple graph, then its chromatic index is either ϱ or ϱ + 1.
Fiorini, Stanley
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On the chromatic index of path decompositions
Discrete Mathematics, 2004 Given a decomposition \(D\) of a graph \(H\) into edge-disjoint copies of a graph \(G\), the chromatic index of \(D\) is the minimum number of colours in any colouring of the copies of \(G\) in \(D\) in which no two copies of \(G\) having a vertex in common get the same colour. For given \(H\) and \(G\), the minimum chromatic index problem asks for the
Peter Danziger +2 more
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Electronic Notes in Discrete Mathematics, 2013 Abstract A b-coloring of the vertices of a graph is a proper coloring where each color class contains a vertex which is adjacent to a vertex in each other color class. The b-chromatic number of G is the maximum integer χ b ( G ) for which G has a b-coloring with χ b ( G ) colors.
Carlos Vinícius G. C. Lima +4 more
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On the Oriented Chromatic Index of Oriented Graphs [PDF]
, 2008 International audienceA homomorphism from an oriented graph G to an oriented graph H is a mapping f from the set of vertices of G to the set of vertices of H such that f(U)f(V) is an arc in H whenever uv is an arc in G. The oriented chromatic index of an
Sopena, Eric +2 more
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A New Proof for a Result on the Inclusion Chromatic Index of Subcubic Graphs
Axioms, 2022 Let G be a graph with a minimum degree δ of at least two. The inclusion chromatic index of G, denoted by χ⊂′(G), is the minimum number of colors needed to properly color the edges of G so that the set of colors incident with any vertex is not contained ...
Lily Chen, Yanyi Li
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