A skew version of the Loebl–Komlós–Sós conjecture
| Autor: | Tereza Klimošová, Václav Rozhoň, Diana Piguet |
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| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Conjecture Applied Mathematics 010102 general mathematics Skew 0102 computer and information sciences 01 natural sciences Graph Extremal graph theory Combinatorics 010201 computation theory & mathematics Discrete Mathematics and Combinatorics Ramsey's theorem 0101 mathematics Mathematics |
| Zdroj: | Electronic Notes in Discrete Mathematics. 61:743-749 |
| ISSN: | 1571-0653 |
| DOI: | 10.1016/j.endm.2017.07.031 |
| Popis: | Loebl, Komlos, and Sos conjectured that any graph such that at least half of its vertices have degree at least k contains every tree of order at most k + 1. We propose a skew version of this conjecture. We consider the class of trees of order at most k + 1 of given skew, that is, such that the sizes of the colour classes of the trees have a given ratio. We show that our conjecture is asymptotically correct for dense graphs. The proof relies on the regularity method. Our result implies bounds on Ramsey number of several trees of given skew. |
| Databáze: | OpenAIRE |
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