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arXiv · 1104.3704

The Bipartite Swapping Trick on Graph Homomorphisms

Yufei Zhao
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Abstract

We provide an upper bound to the number of graph homomorphisms from $G$ to $H$, where $H$ is a fixed graph with certain properties, and $G$ varies over all $N$-vertex, $d$-regular graphs. This result generalizes a recently resolved conjecture of Alon and Kahn on the number of independent sets. We build on the work of Galvin and Tetali, who studied the number of graph homomorphisms from $G$ to $H$ when $H$ is bipartite. We also apply our techniques to graph colorings and stable set polytopes.

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Yufei Zhao. 2011-04-19. The Bipartite Swapping Trick on Graph Homomorphisms. https://doi.org/10.1137/100800415

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