Title: Countable weighted graphs with no unfriendly partitions
|Affiliation:||Technical University of Denmark|
The vertex set of every finite graph can be partitioned into two sets such that each vertex has at least as many vertices in the opposite set as in its own set. Such a partition is called unfriendly. It is known that there are infinite graphs with no unfriendly partition but it is open if every countable graph has an unfriendly partition. In this talk we show that the there are edge-weighted countable graphs with no unfriendly partition.
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