Maximum number of r-edge-colorings such that all copies of Kk are rainbow
Fecha
2021Autor
Materia
Abstract
We consider a version of the Erdős-Rothschild problem for families of graph patterns. For any fixed k ≥ 3, let r0(k) be the largest integer such that the following holds for all 2 ≤ r ≤ r0(k) and all sufficiently large n: The Turán graph Tk-1(n) is the unique n-vertex graph G with the maximum number of r-edge-colorings such that the edge set of any copy of Kk in G is rainbow. We use the regularity lemma of Szemerédi and linear programming to obtain a lower bound on the value of r0(k). For a mor ...
We consider a version of the Erdős-Rothschild problem for families of graph patterns. For any fixed k ≥ 3, let r0(k) be the largest integer such that the following holds for all 2 ≤ r ≤ r0(k) and all sufficiently large n: The Turán graph Tk-1(n) is the unique n-vertex graph G with the maximum number of r-edge-colorings such that the edge set of any copy of Kk in G is rainbow. We use the regularity lemma of Szemerédi and linear programming to obtain a lower bound on the value of r0(k). For a more general family P of patterns of Kk, we also prove that, in order to show that the Turán graph Tk-1(n) maximizes the number of P-free r-edge-colorings over n-vertex graphs, it suffices to prove a related stability result. ...
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Procedia Computer Science. Amsterdam. Vol. 195 (2021), p. 419 - 426
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