From Edge-Coloring to Strong Edge-Coloring

Abstract : In this paper we study a generalization of both proper edge-coloring and strong edge-coloring: k-intersection edge-coloring, introduced by Muthu, Narayanan and Subramanian. In this coloring, the set S(v) of colors used by edges incident to a vertex v does not intersect S(u) on more than k colors when u and v are adjacent. We provide some sharp upper and lower bounds for χ′k-int for several classes of graphs. For l-degenerate graphs we prove that χ′k-int(G)≤(l+1)Δ−l(k−1)−1. We improve this bound for subcubic graphs by showing that χ′2-int(G)≤6. We show that calculating χ′k-int(Kn) for arbitrary values of k and n is related to some problems in combinatorial set theory and we provide bounds that are tight for infinitely many values of n. Furthermore, for complete bipartite graphs we prove that χ′k-int(Kn,m)=⌈mnk⌉. Finally, we show that computing χ′k-int(G) is NP-complete for every k≥1.
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Contributor : Petru Valicov <>
Submitted on : Tuesday, April 21, 2015 - 10:01:43 AM
Last modification on : Monday, August 5, 2019 - 3:26:03 PM

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  • HAL Id : hal-01144153, version 1

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Valentin Borozan, Gerard Jennhwa Chang, Nathann Cohen, Shinya Fujita, Narayanan Narayanan, et al.. From Edge-Coloring to Strong Edge-Coloring. The Electronic Journal of Combinatorics, Open Journal Systems, 2015, 22 (2), pp.P2.9. ⟨hal-01144153⟩

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