The Decomposability of Toroidal Graphs without Adjacent Triangles or Short Cycles

Autor:	Huajing Lu, Fengwei Li
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	toroidal graph defective coloring decomposability defective DP-coloring Mathematics QA1-939
Zdroj:	Axioms, Vol 12, Iss 2, p 173 (2023)
Druh dokumentu:	article
ISSN:	2075-1680
DOI:	10.3390/axioms12020173
Popis:	A graph G has a (d,h)-decomposition if there is a pair (D,F) such that F is a subgraph of G and D is an acyclic orientation of G−E(F), where the maximum degree of F is no more than h and the maximum out-degree of D is no more than d. This paper proves that toroidal graphs having no adjacent triangles are (3,1)-decomposable, and for {i,j}⊆{3,4,6}, toroidal graphs without i- and j-cycles are (2,1)-decomposable. As consequences of these results, toroidal graphs without adjacent triangles are 1-defective DP-4-colorable, and toroidal graphs without i- and j-cycles are 1-defective DP-3-colorable for {i,j}⊆{3,4,6}.
Databáze:	Directory of Open Access Journals
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