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6 papers · 2 filters
Asymptotic Dimension of Minor-Closed Families and Assouad-Nagata Dimension of Surfaces
Marthe Bonamy, Nicolas Bousquet, Louis Esperet +4
The asymptotic dimension is an invariant of metric spaces introduced by Gromov in the context of geometric group theory. In this paper, we study the asymptotic dimension of metric…
A characterization of Sturmian sequences by indistinguishable asymptotic pairs
Sebastián Barbieri, Sébastien Labbé, Štěpán Starosta
We give a new characterization of biinfinite Sturmian sequences in terms of indistinguishable asymptotic pairs. Two asymptotic sequences on a full -shift are indistingu…
Injective edge-coloring of graphs with given maximum degree
Alexandr Kostochka, André Raspaud, Jingwei Xu
A coloring of edges of a graph is injective if for any two distinct edges and , the colors of and are distinct if they are at distance in or in a…
Fractional vertex-arboricity of planar graphs
Marthe Bonamy, František Kardoš, Tom Kelly +1
We initiate a systematic study of the fractional vertex-arboricity of planar graphs and demonstrate connections to open problems concerning both fractional coloring and the size of…
On star edge colorings of bipartite and subcubic graphs
Carl Johan Casselgren, Jonas B. Granholm, André Raspaud
A star edge coloring of a graph is a proper edge coloring with no -colored path or cycle of length four. The star chromatic index of is the minimum number f…
Phylogenetic trees, augmented perfect matchings, and a Thron-type continued fraction (T-fraction) for the Ward polynomials
Andrew Elvey Price, Alan D. Sokal
We find a Thron-type continued fraction (T-fraction) for the ordinary generating function of the Ward polynomials, as well as for some generalizations employing a large (indeed inf…