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arXiv · 2009.06840

Extremal even-cycle-free subgraphs of the complete transposition graphs

Mengyu Cao·Benjian Lv·Kaishun Wang·Sanming Zhou
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Abstract

Given graphs $G$ and $H$, the generalized Turán number ${\rm ex}(G,H)$ is the maximum number of edges in an $H$-free subgraph of $G$. In this paper, we obtain an asymptotic upper bound on ${\rm ex}(CT_n,C_{2l})$ for any $n \ge 3$ and $l\geq2$, where $C_{2l}$ is the cycle of length $2l$ and $CT_n$ is the complete transposition graph which is defined as the Cayley graph on the symmetric group ${\rm S}_n$ with respect to the set of all transpositions of ${\rm S}_n$.

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Mengyu Cao, Benjian Lv, Kaishun Wang, Sanming Zhou. 2020-09-15. Extremal even-cycle-free subgraphs of the complete transposition graphs. https://arxiv.org/abs/2009.06840

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