Unfriendly partitions for graphs not containing a subdivision of an infinite clique
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- Berger, E. Combinatorica (2017) 37: 157. doi:10.1007/s00493-015-3261-1
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We prove that in any graph containing no subdivision of an infinite clique there exists a partition of the vertices into two parts, satisfying the condition that every vertex has at least as many neighbors in the part not containing it as it has in its own part.