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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.CO2025
Planar induced paths via a decomposition into non-crossing ordered graphs
Julien Duron, Hugo Jacob
In any graph, the maximum size of an induced path is bounded by the maximum size of a path. However, in the general case, one cannot find a converse bound, even up to an arbitrary…
math.CO2025
A note on distance-hereditary graphs whose complement is also distance-hereditary
Hugo Jacob
Distance-hereditary graphs are known to be the graphs that are totally decomposable for the split decomposition. We characterise distance-hereditary graphs whose complement is also…