Aubian

Decomposing tournaments into comparability graphs

Announce Type: cross Abstract: In this note, we introduce the \emph{partial order decomposition number} of a digraph $D$, denoted $pod(D)$, defined as the minimum integer $k$ such that $A(D)=A(P_1)\cup\cdots\cup A(P_k)$, where $P_1,\ldots,P_k$ are partial orders on $V(D)$. We prove that $\dic(D)\le \diomega(D)^{pod(D)}$ for every digraph $D$. In particular, every class of digraphs with bounded $pod$ is polynomially $\dic$-bounded. We apply this to tournaments, showing that if $\mathcal C$ is...