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5 papers · 2 filters
Constructing disjoint Steiner trees in Sierpiński graphs
Chenxu Yang, Ping Li, Yaping Mao +2
Let be a graph and with . Then the trees in are \emph{internally disjoint Steiner trees} connecting (or -Stei…
A Polynomial Upper Bound for Poset Saturation
Paul Bastide, Carla Groenland, Maria-Romina Ivan +1
Given a finite poset , we say that a family of subsets of is -saturated if does not contain an induced copy of ,…
Three-cuts are a charm: acyclicity in 3-connected cubic graphs
František Kardoš, Edita Máčajová, Jean Paul Zerafa
Let be a bridgeless cubic graph. In 2023, the three authors solved a conjecture (also known as the -Conjecture) made by Mazzuoccolo in 2013: there exist two perfect matchi…
The structure of quasi-transitive graphs avoiding a minor with applications to the domino problem
Louis Esperet, Ugo Giocanti, Clément Legrand-Duchesne
An infinite graph is quasi-transitive if its vertex set has finitely many orbits under the action of its automorphism group. In this paper we obtain a structure theorem for locally…
Intervals in the greedy Tamari posets
Mireille Bousquet-Mélou, Frédéric Chapoton
We consider a greedy version of the -Tamari order defined on -Dyck paths, recently introduced by Dermenjian. Inspired by intriguing connections between intervals in the ordin…