A Note on Vertex Arboricity of Toroidal Graphs without 7-Cycles
نویسنده
چکیده
The vertex arboricity ρ(G) of a graph G is the minimum number of subsets into which the vertex set V (G) can be partitioned so that each subset induces an acyclic graph. In this paper, it is shown that if G is a toroidal graph without 7-cycles, moreover, G contains no triangular and adjacent 4-cycles, then ρ(G) ≤ 2. Mathematics Subject Classification: Primary: 05C15; Secondary: 05C70
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