2022
DOI: 10.1016/j.disc.2021.112664
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On the signed chromatic number of some classes of graphs

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Cited by 8 publications
(14 citation statements)
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“…Bensmail et al [9] proved that every connected 2-edge-colored graph with maximum degree 3 except the all positive and all negative K 4 admits a homomorphism to T R(SP 5 ), hence χ 2 (D c 3 ) ≤ 12, and χ s (D c…”
Section: Connected 2-edge-colored Graphs With Maximum Degreementioning
confidence: 99%
“…Bensmail et al [9] proved that every connected 2-edge-colored graph with maximum degree 3 except the all positive and all negative K 4 admits a homomorphism to T R(SP 5 ), hence χ 2 (D c 3 ) ≤ 12, and χ s (D c…”
Section: Connected 2-edge-colored Graphs With Maximum Degreementioning
confidence: 99%
“…Observe that, u 1 and v 1 do not need to be distinct from each other or from w′, however, since all three of them are precolored, we may assume they are distinct. After forming the set of admissible colors on u v w , , , induced by the coloring of u v , 1 1 , and w′, respectively, with the updated list, the conditions of Lemma 4.14 (1) with k = 1 are satisfied, implying that this configuration is reducible. □ Lemma 5.7.…”
Section: Reducible Configurationsmentioning
confidence: 99%
“…⧹ contains a one-sided 4-set and we are done by applying Lemma 4.11 (1). Thus we assume be a signed odd cycle where…”
mentioning
confidence: 99%
“…• For 2-edge colored graphs, that is, for (n, m) = (0, 2), (0, 2)-chromatic number 1 and of chromatic number of signed graphs, the use of absolute and relative cliques to establish lower bounds can be observed in the following works: [3,31,34].…”
Section: The Significance Of Relative Cliquesmentioning
confidence: 99%