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Start Over Author "Linzhong Liu" Journal discrete applied mathematics
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2. On the relations between arboricity and independent number or covering number

Author

Jianfang Wang, Zhongfu Zhang, Linzhong Liu, and Jianxun Zhang

Subjects
Vertex (graph theory), Discrete mathematics, Degree (graph theory), Arboricity, Applied Mathematics, Covering number, Graph, Combinatorics, Integer, Independent number, Discrete Mathematics and Combinatorics, Relation, Mathematics
Abstract

In this paper, the following results are obtained: a(G) + β(G) ⩽ p + 1, ⌈p2⌉ ⩽ a(G)β(G), ⌈p2⌉ ⩽ a′(G) + gb′(Ḡ) ⩽ pa′(G) + α′(Ḡ) ⩽ 2⌈p2⌉ (δ ⩽ 1) and all bounds are sharp, where p = ¦V(G)¦, ⌈x⌉ denotes the smallest integer greater than or equal to x, a(G) is the vertex arboricity, a′(G) is the edge arboricity, α′(G) is the edge covering number, β(G) is the vertex independent number, β′(G) is the edge independent number, and δ is the minimum degree of G.

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