8 citations · 20 across the 14 of their papers we have counts for
13 papers · 1 filter
Generalising the achromatic number to Zaslavsky's colourings of signed graphs
Julien Bensmail, François Dross, Nacim Oijid +1
The chromatic number, which refers to the minimum number of colours required to colour the vertices of graphs properly, is one of the most central notions of the graph chromatic th…
1-planar graphs with minimum degree at least 3 have bounded girth
François Dross
We show that every 1-planar graph with minimum degree at least 4 has girth at most , and every 1-planar graph with minimum degree at least 3 has girth at most .
Graphs with the second and third maximum Wiener index over the 2-vertex connected graphs
Stéphane Bessy, François Dross, Martin Knor +1
Wiener index, defined as the sum of distances between all unordered pairs of vertices, is one of the most popular molecular descriptors. It is well known that among 2-vertex connec…
The structure of graphs with given number of blocks and the maximum Wiener index
Stéphane Bessy, François Dross, Katarína Hriňáková +2
The Wiener index (the distance) of a connected graph is the sum of distances between all pairs of vertices. In this paper, we study the maximum possible value of this invariant amo…
Partitioning sparse graphs into an independent set and a graph with bounded size components
Ilkyoo Choi, François Dross, Pascal Ochem
We study the problem of partitioning the vertex set of a given graph so that each part induces a graph with components of bounded order; we are also interested in restricting these…
On the unavoidability of oriented trees
François Dross, Frédéric Havet
A digraph is {\it -unavoidable} if it is contained in every tournament of order . We first prove that every arborescence of order with leaves is -unavoidable…
Vertex partitions of -free planar graphs
François Dross, Pascal Ochem
A graph is -colorable if its vertex set can be partitioned into a graph with maximum degree at most and and a graph with maximum degree at most . We show that…
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…
Partitioning a triangle-free planar graph into a forest and a forest of bounded degree
François Dross, Mickael Montassier, Alexandre Pinlou
An -partition of a graph is a vertex-partition into two sets and such that the graph induced by is a forest and the one induced by is a f…
Colouring Diamond-free Graphs
Konrad K. Dabrowski, François Dross, Daniël Paulusma
The Colouring problem is that of deciding, given a graph and an integer , whether admits a (proper) -colouring. For all graphs up to five vertices, we classify th…
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…
Large induced forests in planar graphs with girth 4 or 5
François Dross, Mickael Montassier, Alexandre Pinlou
We give here some new lower bounds on the order of a largest induced forest in planar graphs with girth and . In particular we prove that a triangle-free planar graph of ord…