# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# Discussiones Mathematicae Graph Theory

Journal Impact Factor (JIF 2023): 0.5

5-year Journal Impact Factor (2023): 0.6

CiteScore (2023): 2.2

SNIP (2023): 0.681

# Discussiones Mathematicae Graph Theory

## Abstract

We extend the notion of a potentially H-graphic sequence as follows. Let A and B be nonnegative integer sequences. The sequence pair S = (A,B) is said to be bigraphic if there is some bipartite graph G = (X∪Y,E) such that A and B are the degrees of the vertices in X and Y, respectively. If S is a bigraphic pair, let σ(S) denote the sum of the terms in A.

Given a bigraphic pair S, and a fixed bipartite graph H, we say that S is potentially H-bigraphic if there is some realization of S containing H as a subgraph. We define σ(H,m,n) to be the minimum integer k such that every bigraphic pair S = (A,B) with |A|= m, |B|= n and σ(S) ≥k is potentially H-bigraphic. In this paper, we determine σ(Ks,t,m,n), σ(Pt,m,n) and σ(C2t,m,n).

Keywords: degree sequence, bipartite graph, potential number.

2000 Mathematics Subject Classification: 05C07, 05C35.

## References

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