Displaying similar documents to “A Constructive Extension of the Characterization on PotentiallyK s , t -Bigraphic Pairs”

On degree sets and the minimum orders in bipartite graphs

Y. Manoussakis, H.P. Patil (2014)

Discussiones Mathematicae Graph Theory

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For any simple graph G, let D(G) denote the degree set {degG(v) : v ∈ V (G)}. Let S be a finite, nonempty set of positive integers. In this paper, we first determine the families of graphs G which are unicyclic, bipartite satisfying D(G) = S, and further obtain the graphs of minimum orders in such families. More general, for a given pair (S, T) of finite, nonempty sets of positive integers of the same cardinality, it is shown that there exists a bipartite graph B(X, Y ) such that D(X)...

A note on degree-continuous graphs

Chiang Lin, Wei-Bo Ou (2007)

Czechoslovak Mathematical Journal

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The minimum orders of degree-continuous graphs with prescribed degree sets were investigated by Gimbel and Zhang, Czechoslovak Math. J. 51 (126) (2001), 163–171. The minimum orders were not completely determined in some cases. In this note, the exact values of the minimum orders for these cases are obtained by giving improved upper bounds.