Random cubic graphs are not homomorphic to the cycle of size 7

Details Random cubic graphs are not homomorphic to the cycle of size 7 Random cubic graphs are not homomorphic to the cycle of size 7

2006-12-31

arxiv.org/abs/math/0701013v1

J. Combin. Theory Ser. B 93(2) (2005) pp. 319-325

Mathematics

Combinatorics

Scientific paper

We prove that a random cubic graph almost surely is not homomorphic to a
cycle of size 7. This implies that there exist cubic graphs of arbitrarily high
girth with no homomorphisms to the cycle of size 7.

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