Every rayless graph has an unfriendly partition
Henning Bruhn, Reinhard Diestel, Agelos Georgakopoulos, Philipp, Spr\"ussel
TL;DR
This paper proves that all rayless graphs can be partitioned into two parts such that each vertex has at least as many neighbors in the opposite part, extending understanding of graph partition properties.
Contribution
The paper establishes that every rayless graph admits an unfriendly partition, a significant extension in the theory of graph partitions.
Findings
All rayless graphs have an unfriendly partition
The result applies to infinite graphs with no rays
Advances the theory of graph partitions
Abstract
We prove that every rayless graph has an unfriendly partition.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Graph theory and applications