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math.CO2026
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…
math.CO2024
Graphs without a 3-connected subgraph are 4-colorable
Ãdouard Bonnet, Carl Feghali, Tung Nguyen +4
In 1972, Mader showed that every graph without a 3-connected subgraph is 4-degenerate and thus 5-colorable}. We show that the number 5 of colors can be replaced by 4, which is best…