Results 281 to 290 of about 39,087 (298)

Resolving edge colorings in graphs.

Ars Comb., 2005
By \(\chi_{re}(G)\) we mean the resolving edge chromatic number of a connected graph \(G\). The following upper bounds are proved. If \(G\) is of size \(m\geq 3\) and diameter \(d\), then \(\chi_{re}(G)\leq m-d+3\), where \(\chi_{re}(G)=m-d+3\) if and only if \(G\) is a path of size \(m\geq 3\).
Gary Chartrand, Varaporn Saenpholphat, Ping Zhang 0004   +2 more
openaire   +1 more source

A note on edge coloring of graphs.

Ars Comb., 2015
Summary: Let \(G\) be a graph of minimum degree \(\delta (G)\). R. P. Gupta proved the two following interesting results: 1) A bipartite graph \(G\) has a \(\delta \)-edge-coloring in which all \(\delta \) colors appear at each vertex. 2) If \(G\) is a simple graph with \(\delta (G)>1\), then \(G\) has a \((\delta -1)\)-edge-coloring in which all ...
Saieed Akbari, Moharram N. Iradmusa, M. Jamaali   +2 more
openaire   +1 more source

On the two‐edge‐colorings of perfect graphs

Journal of Graph Theory, 1995
AbstractWe investigate the conjecture that a graph is perfect if it admits a two‐edge‐coloring such that two edges receive different colors if they are the nonincident edges of a P4 (chordless path with four vertices). Partial results on this conjecture are given in this paper. © 1995 John Wiley & Sons, Inc.
openaire   +2 more sources

Edge Coloring on Dynamic Graphs

2023
Zhepeng Huang, Long Yuan 0001, Haofei Sui, Zi Chen 0003, Shiyu Yang, Jianye Yang 0001   +5 more
openaire   +1 more source

A classification of edge-colored graphs based on properly colored walks

Discrete Applied Mathematics, 2020
Ruonan Li, Shenggui Zhang
exaly  

Disjoint properly colored cycles in edge-colored complete bipartite graphs

Discrete Mathematics, 2023
Kiyoshi Yoshimoto
exaly  

Graph Edge Coloring and Extensions of Edge Colorings

This dissertation explores two main questions which may be framed in terms of graph edge-coloring. First, an assignment of $k$ colors to the edges of the complete bipartite graph $K_{n,n}$ corresponds to an assignment of $k$ symbols to the cells of an $n\times n$ array.
openaire   +1 more source

Cycles and paths in edge‐colored graphs with given degrees

Journal of Graph Theory, 2010
M Karpinski, Y Manoussakis
exaly  

On s-t paths and trails in edge-colored graphs

Electronic Notes in Discrete Mathematics, 2009
Laurent Gourvès, Adria Lyra, Jérôme Monnot   +2 more
exaly  

On Edge-Colored Graphs Covered by Properly Colored Cycles

Graphs and Combinatorics, 2005
Herbert Fleischner, Stefan Szeider, Szeider Stefan   +2 more
exaly