Name: Infinite friendship graphs with infinite parameters
Keywords: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Theoretical Computer Science

descriptionPublicationkeyboard_double_arrow_right Article 01 May 1991 English Publisher:Elsevier BVJournal:Journal of Combinatorial Theory, Series B, volume 52, pages 30-41 (issn: 0095-8956,

Authors: E. C. Milner; Geňa Hahn; Robert E. Woodrow;

doi: 10.1016/0095-8956(91)90087-z

Infinite friendship graphs with infinite parameters

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Abstract

AbstractWe study infinite graphs in which every set of κ vertices has exactly λ common neighbours. We prove that there exist 2σ such graphs of each infinite order σ if κ is finite and that for κ infinite there are 2λ graphs of order λ and none of cardinality greater than λ (assuming the GCH). Further, we show that all a priori admissible chromatic numbers are in fact possible for such graphs.

Related Organizations

University of Montreal
Canada
University of Calgary
Canada

Keywords

Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Theoretical Computer Science

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