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Generalised Ramsey numbers for two sets of cycles
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2018 (English)In: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 238, p. 86-94Article in journal (Refereed) Published
Abstract [en]

Let C-1 and C-2 be two sets of cycles. We determine all generalised Ramsey numbers R(C-1, C-2) such that C-1 or C-2 contains a cycle of length at most 6. This generalises previous results of Erdos, Faudree, Rosta, Rousseau, and Schelp. Furthermore, we give a conjecture for the general case. We also provide a complete classification of most (C-1, C-2)-critical graphs such that C-1 or C-2 contains a cycle of length at most 5. For length 4, this is an easy extension of a recent result of Wu, Sun, and Radziszowski, in which vertical bar C-1 vertical bar = vertical bar C-2 vertical bar = 1. For lengths 3 and 5, our results are new also in this special case. (C) 2017 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV , 2018. Vol. 238, p. 86-94
Keywords [en]
Generalised Ramsey number; Critical graph; Cycle; Set of cycles
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-147100DOI: 10.1016/j.dam.2017.12.019ISI: 000427218900009OAI: oai:DiVA.org:liu-147100DiVA, id: diva2:1199558
Available from: 2018-04-20 Created: 2018-04-20 Last updated: 2018-05-18

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