1983
DOI: 10.1016/0196-6774(83)90032-9
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NP completeness of finding the chromatic index of regular graphs

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Cited by 164 publications
(101 citation statements)
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“…Holyer [12] showed that 3-Coloring is NP-complete on line graphs. Later, Leven and Galil [18] extended this result by showing that k-Coloring is also NP-complete on line graphs for k ≥ 4. Because line graphs are claw-free, i.e., they have no induced K 1,3 , we find that for k ≥ 3, the k-Coloring problem is NP-complete for the class of H-free graphs if H is a forest that contains a vertex with degree at least 3.…”
Section: Theorem 1 ([15])mentioning
confidence: 86%
See 1 more Smart Citation
“…Holyer [12] showed that 3-Coloring is NP-complete on line graphs. Later, Leven and Galil [18] extended this result by showing that k-Coloring is also NP-complete on line graphs for k ≥ 4. Because line graphs are claw-free, i.e., they have no induced K 1,3 , we find that for k ≥ 3, the k-Coloring problem is NP-complete for the class of H-free graphs if H is a forest that contains a vertex with degree at least 3.…”
Section: Theorem 1 ([15])mentioning
confidence: 86%
“…As explained in Section 1, the 5-Coloring problem is NP-complete for Hfree graphs whenever H is not a linear forest, due to results of Kamiński and Lozin [13] and Leven and Galil [18]. Consequently, List 5-Coloring is NPcomplete for such graph classes.…”
Section: Construction Of Gmentioning
confidence: 99%
“…[18]), states that every line graph is k-choosable if and only if it is k-colorable. It is known that the k-Coloring problem is NP-complete on line graphs for all k ≥ 3 [21,24]. This implies that k-Choosability is NP-complete on line graphs for every k ≥ 3, unless the List Coloring Conjecture is false.…”
Section: Introductionmentioning
confidence: 93%
“…We note that these graphs were used by Leven & Galil (1983) to reduce the edge coloring problem of multigraphs to the edge coloring of simple graphs. Vertices R s and Q t have degree k, while vertices P t have degree 1; therefore, by the following lemma, the k edges (Q t , P t ) have pairwise different colors in every k-edge-coloring of I k .…”
Section: Graphs With S (G) > χ (G)mentioning
confidence: 99%
“…has the same complexity as "Is χ (G) ≤ k?" and the latter problem is known to be NPcomplete for every k ≥ 3 (Holyer 1981;Leven & Galil 1983). However, if we want to prove that edge strength is Θ p 2 -complete (that is, harder than the chromatic index problem), then necessarily we have to consider graphs where the edge strength and the chromatic index are not the same.…”
Section: Introductionmentioning
confidence: 99%