Singular Ramsey and Turán numbers

Authors

Yair Caro, University of Haifa-OranimFollow
Zsolt Tuza, Alfréd Rényi Institute of Mathematics, Budapest, and University of Pannonia, VeszprémFollow

Abstract

We say that a subgraph F of a graph G is singular if the degrees d_G(v) are all equal or all distinct for the vertices v ∈ V (F). The singular Ramsey number Rs(F) is the smallest positive integer n such that, for every m at least n, in every edge 2-coloring of K_m, at least one of the color classes contains F as a singular subgraph. In a similar flavor, the singular Turán number Ts(n,F) is defined as the maximum number of edges in a graph of order n, which does not contain F as a singular subgraph. In this paper we initiate the study of these extremal problems. We develop methods to estimate Rs(F) and Ts(n,F), present tight asymptotic bounds and exact results.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Caro, Yair and Tuza, Zsolt (2019) "Singular Ramsey and Turán numbers," Theory and Applications of Graphs: Vol. 6: Iss. 1, Article 1.
DOI: 10.20429/tag.2019.060101
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol6/iss1/1