Year: 2025
Type: preprint
Abstract: For a family of graphs $\cF$, a graph is called $\cF$-free if it does not contain any member of $\cF$ as a subgraph. Given a collection of graphs $(G_1,\ldots,G_t)$ on the same vertex set $V$ of size $n$, a rainbow graph on $V$ is obtained by taking at most one edge from each $G_i$. We say that a collection is rainbow $\cF$-free if it contains no rainbow copy of any member of $\cF$. In this paper, we study the maximum values of $min_{i\in [t]}|E(G_i)|$, $\sum_{i=1}^{t}|E(G_i)|$ and $\prod_{i=1}^{t}|E(G_i)|$ among rainbow $\{F,M_{s+1}\}$-free collections $(G_1,\ldots,G_t)$ on $n$ vertices.
Source: arXiv (Cornell University)
Authors: Gerbner, Dániel, Miao, Shujing
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2375677999, G3255774899, G712529603
OpenAlex ID: W4415023902
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