Caro, Yair and Tuza, Zsolt (2019) Singular Ramsey and Turán numbers. Theory and Applications of Graphs, TAG, 6 (1). ISSN 2470-9859
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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 ≥ 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. © 2019 Georgia Southern University. All rights reserved.
| Item Type: | Article |
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| Additional Information: | University of Haifa-Oranim, Israel Alfréd Rényi Institute of Mathematics, Budapest, Hungary University of Pannonia, Veszprém, Hungary Export Date: 30 October 2019 Funding details: Office of Research, Innovation and Economic Development, California State Polytechnic University, Pomona Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, SNN 129364 Funding text 1: Research of the second author was supported in part by the National Research, Development and Innovation Office --NKFIH under the grant SNN 129364. |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 16 Jan 2020 12:46 |
| Last Modified: | 16 Jan 2020 12:46 |
| URI: | http://real.mtak.hu/id/eprint/105501 |
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