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Crossing tournaments are polynomially -bounded
Lila Crew, Xinyue Fan, Hidde Koerts +2
Given a tournament , Aboulker, Aubian, Charbit, and Lopes (2023) defined its clique number as the minimum clique number of a backedge graph of , and raised the que…
Decomposing tournaments into comparability graphs
Pierre Aboulker, Logan Crew, Julien Duron +7
In this note, we introduce the \emph{partial order decomposition number} of a digraph , denoted , defined as the minimum integer such that $A(D)=A(P_1)\cup\cdots\cup…
Homomorphism counting for immersion-closed classes is not isomorphism
Andrea Jiménez, Benjamin Moore, Daniel A. Quiroz +1
Lovász proved that two graphs and are isomorphic if for all graphs , where denotes the number of homomorphisms from to $G_2…
Characterizing Large Clique Number in Tournaments
Logan Crew, Xinyue Fan, Hidde Koerts +2
Aboulker, Aubian, Charbit, and Lopes (2023) defined the clique number of a tournament to be the minimum clique number of one of its backedge graphs. Here we show that if is a t…