Generalized Split Graphs and Ramsey Numbers

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

A graphGis called a (p,q)-split graph if its vertex set can be partitioned intoA,Bso that the order of the largest independent set inAis at mostpand the order of the largest complete subgraph inBis at mostq. Applying a well-known theorem of Erdos and Rado forΔ-systems, it is shown that for fixedp,q, (p,q)-split graphs can be characterized by excluding a finite set of forbidden subgraphs, called (p,q)-split critical graphs. The order of the largest (p,q)-split critical graph,f(p,q), relates to classical Ramsey numbersR(s,t) through the inequalities2F(F(R(p+2,q+2)))+1≥f(p,q)≥R(p+2,q+2)-1whereF(t) is the smallest number oft-element sets ensuring at+1-elementΔ-system. Apart fromf(1,1)=5, all values off(p,q) are unknown.

Original languageEnglish
Pages (from-to)255-261
Number of pages7
JournalJournal of Combinatorial Theory, Series A
Volume81
Issue number2
DOIs
Publication statusPublished - Feb 1998

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Split Graph
Ramsey number
Critical Graph
Forbidden Subgraph
Independent Set
Erdös
Large Set
Finite Set
Subgraph
Unknown
Vertex of a graph
Theorem

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Generalized Split Graphs and Ramsey Numbers. / Gyárfás, A.

In: Journal of Combinatorial Theory, Series A, Vol. 81, No. 2, 02.1998, p. 255-261.

Research output: Contribution to journalArticle

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