3 citations · 8 across the 5 of their papers we have counts for
7 papers · 1 filter
Homothetic triangle representations of planar graphs
Daniel Gonçalves, Benjamin Lévêque, Alexandre Pinlou
We prove that every planar graph is the intersection graph of homothetic triangles in the plane.
Oriented coloring of graphs with low maximum degree
Pascal Ochem, Alexandre Pinlou
Duffy et al. [C. Duffy, G. MacGillivray, and É. Sopena, Oriented colourings of graphs with maximum degree three and four, Discrete Mathematics, 342(4), p. 959--974, 2019] recently…
A lower bound on the order of the largest induced linear forest in triangle-free planar graphs
François Dross, Mickael Montassier, Alexandre Pinlou
We prove that every triangle-free planar graph of order and size has an induced linear forest with at least vertices, and thus at least $\frac{5n + 8}{…
Partitioning sparse graphs into an independent set and a forest of bounded degree
François Dross, Mickael Montassier, Alexandre Pinlou
An -partition of a graph is a partition of the vertices of the graph into two sets and , such that is an independent set and induces a forest…
A lower bound on the order of the largest induced forest in planar graphs with high girth
François Dross, Mickael Montassier, Alexandre Pinlou
We give here new upper bounds on the size of a smallest feedback vertex set in planar graphs with high girth. In particular, we prove that a planar graph with girth and size $m…
Graphs with maximum degree D at least 17 and maximum average degree less than 3 are list 2-distance (D+2)-colorable
Marthe Bonamy, Benjamin Lévêque, Alexandre Pinlou
For graphs of bounded maximum average degree, we consider the problem of 2-distance coloring. This is the problem of coloring the vertices while ensuring that two vertices that are…