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6 papers · 2 filters
A -analog of the Markoff injectivity conjecture holds
Sebastien Labbé, Mélodie Lapointe, Wolfgang Steiner
The elements of Markoff triples are given by coefficients in certain matrix products defined by Christoffel words, and the Markoff injectivity conjecture, a long-standing open prob…
Sparse graphs with bounded induced cycle packing number have logarithmic treewidth
Marthe Bonamy, Édouard Bonnet, Hugues Déprés +5
A graph is -free if it does not contain pairwise vertex-disjoint and non-adjacent cycles. We prove that "sparse" (here, not containing large complete bipartite g…
Disjoint odd circuits in a bridgeless cubic graph can be quelled by a single perfect matching
František Kardoš, Edita Máčajová, Jean Paul Zerafa
Let be a bridgeless cubic graph. The Berge--Fulkerson Conjecture (1970s) states that admits a list of six perfect matchings such that each edge of belongs to exactly tw…
On a faithful representation of Sturmian morphisms
Jana Lepšová, Edita Pelantová, Štěpán Starosta
The set of morphisms mapping any Sturmian sequence to a Sturmian sequence forms together with composition the so-called monoid of Sturm. For this monoid, we defne a faithful repres…
Tiered trees and Theta operators
Michele D'Adderio, Alessandro Iraci, Yvan LeBorgne +2
In [Dugan-Glennon-Gunnells-Steingrimsson-2019], the authors introduce tiered trees to define combinatorial objects counting absolutely indecomposable representations of certain qui…
Quasisymmetric functions distinguishing trees
Jean-Christophe Aval, Karimatou Djenabou, Peter R. W. McNamara
A famous conjecture of Stanley states that his chromatic symmetric function distinguishes trees. As a quasisymmetric analogue, we conjecture that the chromatic quasisymmetric funct…