Combinatorica

, Volume 37, Issue 2, pp 157–166

Unfriendly partitions for graphs not containing a subdivision of an infinite clique

Original Paper

DOI: 10.1007/s00493-015-3261-1

Cite this article as:
Berger, E. Combinatorica (2017) 37: 157. doi:10.1007/s00493-015-3261-1
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Abstract

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.

Mathematics Subject Classification (2000)

05C63 

Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Mathematics Faculty of ScienceUniversity of HaifaHaifaIsrael

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