The Bipartite Swapping Trick on Graph Homomorphisms

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 w...

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Bibliographic Details
Main Author: Zhao, Yufei (Contributor)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: Society for Industrial and Applied Mathematics, 2011-09-28T19:02:19Z.
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Online Access:Get fulltext
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100 1 0 |a Zhao, Yufei  |e author 
100 1 0 |a Massachusetts Institute of Technology. Department of Mathematics  |e contributor 
100 1 0 |a Zhao, Yufei  |e contributor 
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245 0 0 |a The Bipartite Swapping Trick on Graph Homomorphisms 
260 |b Society for Industrial and Applied Mathematics,   |c 2011-09-28T19:02:19Z. 
856 |z Get fulltext  |u http://hdl.handle.net/1721.1/66106 
520 |a 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 G is bipartite. We also apply our techniques to graph colorings and stable set polytopes. 
520 |a Massachusetts Institute of Technology. Undergraduate Research Opportunities Program 
546 |a en_US 
655 7 |a Article 
773 |t SIAM Journal on Discrete Mathematics