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• # Artykuł - szczegóły

## Discussiones Mathematicae Graph Theory

2017 | 37 | 1 | 251-259

## A Constructive Extension of the Characterization on PotentiallyKs , t-Bigraphic Pairs

EN

### Abstrakty

EN
Let Ks,t be the complete bipartite graph with partite sets of size s and t. Let L1 = ([a1, b1], . . . , [am, bm]) and L2 = ([c1, d1], . . . , [cn, dn]) be two sequences of intervals consisting of nonnegative integers with a1 ≥ a2 ≥ . . . ≥ am and c1 ≥ c2 ≥ . . . ≥ cn. We say that L = (L1; L2) is potentially Ks,t (resp. As,t)-bigraphic if there is a simple bipartite graph G with partite sets X = {x1, . . . , xm} and Y = {y1, . . . , yn} such that ai ≤ dG(xi) ≤ bi for 1 ≤ i ≤ m, ci ≤ dG(yi) ≤ di for 1 ≤ i ≤ n and G contains Ks,t as a subgraph (resp. the induced subgraph of {x1, . . . , xs, y1, . . . , yt} in G is a Ks,t). In this paper, we give a characterization of L that is potentially As,t-bigraphic. As a corollary, we also obtain a characterization of L that is potentially Ks,t-bigraphic if b1 ≥ b2 ≥ . . . ≥ bm and d1 ≥ d2 ≥ . . . ≥ dn. This is a constructive extension of the characterization on potentially Ks,t-bigraphic pairs due to Yin and Huang (Discrete Math. 312 (2012) 1241–1243).

EN

251-259

wydano
2017-02-01
otrzymano
2015-07-06
poprawiono
2016-04-13
zaakceptowano
2016-04-13
online
2017-01-13

### Twórcy

autor
• Department of Mathematics, College of Information Science and Technology, Hainan University, Haikou 570228, P.R.
autor
• Department of Mathematics, College of Information Science and Technology, Hainan University, Haikou 570228, P.R.