On linear vertex‐arboricity of complementary graphs | Zendy

Alavi Yousef | Zendy; Liu Jiuqiang | Zendy; Wang Jianfang | Zendy

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On linear vertex‐arboricity of complementary graphs

Author(s) -

Alavi Yousef,

Liu Jiuqiang,

Wang Jianfang

Publication year - 1994

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.3190180309

Subject(s) - arboricity , combinatorics , mathematics , vertex (graph theory) , degeneracy (biology) , graph , bound graph , discrete mathematics , graph power , line graph , planar graph , bioinformatics , biology

The linear vertex‐arboricity ρ( G ) of a graph G is defined to be the minimum number of subsets into which the vertex set of G can be partitioned such that each subset induces a linear forest. In this paper, we give the sharp upper and lower bounds for the sum and product of linear vertex‐arboricities of a graph and its complement. Specifically, we prove that for any graph G of order p .and for any graph G of order p = (2 n + 1) 2 , where n ≅ Z + , 2 n + 2 ≦ ρ( G ) + ρ( G ).

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