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arXiv · 1712.07026

Homomorphism thresholds for odd cycles

Oliver Ebsen·Mathias Schacht
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Abstract

The interplay of minimum degree conditions and structural properties of large graphs with forbidden subgraphs is a central topic in extremal graph theory. For a given graph $F$ we define the homomorphism threshold as the infimum over all $\alpha\in[0,1]$ such that every $n$-vertex $F$-free graph $G$ with minimum degree at least $\alpha n$ has a homomorphic image $H$ of bounded order (independent of $n$), which is $F$-free as well. Without the restriction of $H$ being $F$-free we recover the definition of the chromatic threshold, which was determined for every graph $F$ by Allen et al. [Adv. Math. 235 (2013), 261-295]. The homomorphism threshold is less understood and we address the problem for odd cycles.

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BibTeXRIS

Oliver Ebsen, Mathias Schacht. 2017-12-19. Homomorphism thresholds for odd cycles. https://doi.org/10.1007/s00493-019-3920-8

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