Results 21 to 30 of about 4,890 (237)
On the Strong Chromatic Index of Sparse Graphs
The Electronic Journal of Combinatorics, 2018 The strong chromatic index of a graph $G$, denoted $\chi'_s(G)$, is the least number of colors needed to edge-color $G$ so that edges at distance at most two receive distinct colors. The strong list chromatic index, denoted $\chi'_{s,\ell}(G)$, is the least integer $k$ such that if arbitrary lists of size $k$ are assigned to each edge then $G$ can be ...
Philip DeOrsey +9 more
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Strong chromatic index of subcubic planar multigraphs [PDF]
European Journal of Combinatorics, 2015 arXiv admin note: text overlap with arXiv:1506 ...
Alexandr Kostochka +5 more
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The strong chromatic index of sparse graphs [PDF]
Information Processing Letters, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michał Dębski +2 more
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The Strong Chromatic Index of Random Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2005 The strong chromatic index of a graph $G$, denoted by $\chi_s(G)$, is the minimum number of colors needed to color its edges so that each color class is an induced matching. In this paper we analyze the asymptotic behavior of this parameter in a random graph $G(n,p)$, for two regions of the edge probability $p=p(n)$.
Alan Frieze +2 more
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On the precise value of the strong chromatic index of a planar graph with a large girth [PDF]
Discrete Applied Mathematics, 2018 A strong $k$-edge-coloring of a graph $G$ is a mapping from $E(G)$ to $\{1,2,\ldots,k\}$ such that every pair of distinct edges at distance at most two receive different colors. The strong chromatic index $χ'_s(G)$ of a graph $G$ is the minimum $k$ for which $G$ has a strong $k$-edge-coloring.
Gerard J. Chang, Guan-Huei Duh
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The Strong Chromatic Index of Complete Halin Graphs
MathematicsThe strong edge coloring of a graph G is an assignment of colors to the edges of G such that two distinct edges are colored differently if they are incident to a common edge or share an endpoint. The strong chromatic index of a graph G, denoted by χs′(G),
Zhiwei Bi, Yunfang Tang
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The strong chromatic index of $K_{t,t}$-free graphs [PDF]
CoRRA strong edge coloring of a graph $G$ is an edge coloring $ϕ\,:\,E(G) \rightarrow \mathbb N$ such that each color class forms an induced matching in $G$. The strong chromatic index of $G$, written $χ'_s(G)$, is the minimum number of colors needed for a strong edge coloring of $G$. Erdős and Nešetřil conjectured in 1985 that if $G$ has maximum degree $d$
Richard Bi +3 more
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The strong chromatic index of a class of graphs
Discrete Mathematics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wensong Lin
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A Bound on the Strong Chromatic Index of a Graph
Journal of Combinatorial Theory, Series B, 1997 The strong chromatic index \(s\chi'(G)\) of a graph \(G\) is the minimum number of colors in a proper edge coloring of a graph in which no edge is adjacent to an edge of the same color. It is proved that \(s\chi'(G)\leq 1.998\Delta^2\), where \(\Delta\) is the maximum degree of a vertex of \(G\). This answers a question of Erdös and Nešetřil, which was
Michael Molloy, Bruce Reed
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Strong chromatic index of subset graphs [PDF]
Journal of Graph Theory, 1997 A coloring of the edges of a graph is called a strong edge coloring if the edges in each color form an induced matching. The strong chromatic index \(sq(G)\) of a graph \(G\) is the smallest number of colors in any strong coloring. A conjecture of Brualdi and Quinn states that if \(G\) is a bipartite graphs, with parts \(X\) and \(Y\), then \(sq(G)\leq\
Jennifer J. Quinn, Arthur T. Benjamin
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