An extremal problem on potentially Kr,s-graphic sequences

Authors:
Jian-Hua Yin;Jiong-Sheng Li
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China and Department of Mathematics, Quanzhou Teachers College, Quanzhou, Fujian ...;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
Venue:
Discrete Mathematics
Year:
2003

Citing 2
Cited 1

An external problem on the potentially Pk-graphic sequences

Discrete Mathematics - Special issue on Combinatorics and Application
The smallest degree sum that yields potentially Pk-graphical sequences

Journal of Graph Theory

A variation of a classical Turán-type extremal problem

European Journal of Combinatorics

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Abstract

We consider a variation of a classical Turán-type extremal problem (F. Chung, R. Graham, Erdös on Graphs: His Legacy of Unsolved Problems, AK Peters Ltd., Wellesley, 1998, Chapter 3) as follows: Determine the smallest even integer σ(Kr,s,n) such that every n-term graphic sequence π = (d1,d2,.....,dn) with term sum σ(π) = d1 +d2+....+dn ≥ σ(Kr,s,n) is potentially Kr,s-graphic, where Kr,s is a r × s complete bipartite graph, i.e., π has a realization G containing Kr,s as its subgraph. In this paper, we first give sufficient conditions for a graphic sequence being potentially Kr,s-graphic, and then we determine σ(Kr,r ,n) for r = 3, 4.