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math.CO2019
Progress towards Nash-Williams' Conjecture on Triangle Decompositions
Michelle Delcourt, Luke Postle
Partitioning the edges of a graph into edge disjoint triangles forms a triangle decomposition of the graph. A famous conjecture by Nash-Williams from 1970 asserts that any sufficie…
math.CO2019
Bounding the number of cycles in a graph in terms of its degree sequence
Zdeněk Dvořák, Natasha Morrison, Jonathan A. Noel +2
We give an upper bound on the number of cycles in a simple graph in terms of its degree sequence, and apply this bound to resolve several conjectures of Király and Arman and Tsatur…
math.CO2019
Linear-Time and Efficient Distributed Algorithms for List Coloring Graphs on Surfaces
Luke Postle
In 1994, Thomassen proved that every planar graph is 5-list-colorable. In 1995, Thomassen proved that every planar graph of girth at least five is 3-list-colorable. His proofs natu…