Showing papers on "Edge coloring published in 1981"
TL;DR: It is shown that it is NP-complete to determine the chromatic index of an arbitrary graph, even for cubic graphs.
Abstract: We show that it is NP-complete to determine the chromatic index of an arbitrary graph. The problem remains NP-complete even for cubic graphs.
1,373 citations
TL;DR: A simple linear algorithm is presented for coloring planar graphs with at most five colors using a recursive reduction of a graph involving the deletion of a vertex of degree 6 or less possibly together with the identification of its several neighbors.
63 citations
TL;DR: The problem of how ''near'' the authors can come to a n-coloring of a given graph is investigated and an @W(epn) deterministic algorithm for finding such an n-color assignment is exhibited.
40 citations
TL;DR: In this paper, an O(n 4 )-coloring algorithm for claw-free perfect graphs is presented, which shows that the size of a minimum coloring is equal to the maximum clique for graphs containing no claws, odd holes or odd antiholes.
Abstract: An O(n4) minimum coloring algorithm on claw-free perfect graphs is presented. The algorithm proceeds recursively as follows. Let x be any vertex of G. Having colored the subgraph G\x using no more than ω(G) (the size of a maximum clique in G) colors, the algorithm shows how to color G using no more than ω(G) colors. The algorithm demonstrates that the size of a minimum coloring is equal to the size of a maximum clique for graphs containing no claws, odd holes or odd anti-holes, hence it provides an alternative proof that the strong perfect graph conjecture is true for claw-free graphs.
22 citations
TL;DR: It is proved that if σ (G) ≤ 4, G is edge colorable with 4 colors, and that a similar result for maps G with σ(G) ≥ 5 would imply the Four-Color Theorem.
Abstract: A (plane) 4-regular map G is called C-simple if it arises as a superposition of simple closed curves (tangencies are not allowed); in this case σ (G) is the smallest integer k such that the curves of G can be colored with k colors in such a way that no two curves of the same color intersect. We prove that if σ (G) ≤ 4, G is edge colorable with 4 colors. Moreover we show that a similar result for maps G with σ(G) ≤ 5 would imply the Four-Color Theorem.
10 citations
TL;DR: The process introduced by E. Johnson for constructing connected cubic graphs can be modified so as to obtain restricted classes of cubic graphs, in particular, those defined by their Chromatic number or their chromatic index.
4 citations
Proceedings Article•
1 Jan 1981
2 citations
TL;DR: A proof of that conjecture and a corollary that helps determine the chromatic index of some graphs with 2s points and maximum degree 2s − 2 are presented.
Abstract: Vizing's Theorem states that any graph G has chromatic index either the maximum degree Δ(G) or Δ(G) + 1. If G has 2s + 1 points and Δ(G) = 2s, a well-known necessary condition for the chromatic index to equal 2s is that G have at most 2s2 lines. Hilton conjectured that this condition is also sufficient. We present a proof of that conjecture and a corollary that helps determine the chromatic index of some graphs with 2s points and maximum degree 2s − 2.