【摘 要】
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Let G be a graph of order n ≥ 6 with minimum degree δ(G) ≥ 4.Arkin and Hassin (Graph partitions with minimum degree constraints, Discrete Mathematics, 190(19
【机 构】
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DepartmentofMathematics,NanjingUniversity
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Let G be a graph of order n ≥ 6 with minimum degree δ(G) ≥ 4.Arkin and Hassin (Graph partitions with minimum degree constraints, Discrete Mathematics, 190(1998),55-65) conjectured that there exists a bipartition S,T of V(G) such that [n/2]-2 ≤|S|, |T| ≤ [n/2] + 2 and the minimum degrees in the subgraphs induced by S and T are at least two.In this talk, we first show that G has a bipartition such that the minimum degree in each part is at least two, and then prove that the conjecture is true if the complement of G contains no complete bipartite graph K3x, where r =[n/2]-3.
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