Myungho Choi, Minki Kwak, Suh-Ryung Kim
Published 2020-09-21Version 1
In this paper, we show that a connected triangle-free graph is the competition graph of a $k$-partite tournament if and only if $k \in \{3,4,5\}$, and a disconnected triangle-free graph is the competition graph of a $k$-partite tournament if and only if $k \in \{2,3,4\}$. Then we list all the triangle-free graphs in each case.
Comments: 26 pages, 12 figures
Multipartite tournaments whose competition graphs are complete
On the competition graphs of $d$-partial orders
Using $p$-row graphs to study $p$-competition graphs
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