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).
@article{bwmeta1.element.doi-10_7151_dmgt_1928,
author = {Ji-Yun Guo and Jian-Hua Yin},
title = {A Constructive Extension of the Characterization on PotentiallyK s , t -Bigraphic Pairs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {251-259},
zbl = {1354.05030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1928}
}
Ji-Yun Guo; Jian-Hua Yin. A Constructive Extension of the Characterization on PotentiallyK s , t -Bigraphic Pairs. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 251-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1928/