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5 papers · 2 filters
Combinatorial study of graphs arising from the Sachdev-Ye-Kitaev model
Éric Fusy, Luca Lionni, Adrian Tanasa
We consider the graphs involved in the theoretical physics model known as the colored Sachdev-Ye-Kitaev (SYK) model. We study in detail their combinatorial properties at any order…
The Hopf monoid of hypergraphs and its sub-monoids: basic invariant and reciprocity theorem
Jean-Christophe Aval, Théo Karaboghossian, Adrian Tanasa
In arXiv:1709.07504 Ardila and Aguiar give a Hopf monoid structure on hypergraphs as well as a general construction of polynomial invariants on Hopf monoids. Using these results, w…
On the total neighbour sum distinguishing index of graphs with bounded maximum average degree
Hervé Hocquard, Jakub Przybyło
A proper total -colouring of a graph is an assignment of colours to the edges and the vertices of such that no two adjacent edge…
The generating function of planar Eulerian orientations
Mireille Bousquet-Mélou, Andrew Elvey Price
The enumeration of planar maps equipped with an Eulerian orientation has attracted attention in both combinatorics and theoretical physics since at least 2000. The case of 4-valent…
Distributed coloring in sparse graphs with fewer colors
Pierre Aboulker, Marthe Bonamy, Nicolas Bousquet +1
This paper is concerned with efficiently coloring sparse graphs in the distributed setting with as few colors as possible. According to the celebrated Four Color Theorem, planar gr…