30 citations · 45 across the 14 of their papers we have counts for
14 papers
Reed's Conjecture on hole expansions
Jean-Luc Fouquet, Jean-Marie Vanherpe
In 1998, Reed conjectured that for any graph , , where , , and respectively denote the chromatic number, the c…
Reed's conjecture on some special classes of graphs
Jean-Luc Fouquet, Jean-Marie Vanherpe
Reed conjectured that for any graph , , where , , and respectively denote the chromatic number, the clique numbe…
Tools for parsimonious edge-colouring of graphs with maximum degree three
Jean-Luc Fouquet, Jean-Marie Vanherpe
The notion of a -minimum edge-colouring was introduced by J-L. Fouquet (in his french PhD Thesis \cite{FouPhD}). Here we present some structural properties of -minimum edge-c…
On Compatible Normal Odd Partitions in Cubic Graphs
Jean-Luc Fouquet, Jean-Marie Vanherpe
A normal odd partition T of the edges of a cubic graph is a partition into trails of odd length (no repeated edge) such that each vertex is the end vertex of exactly one trail of t…
A new bound for parsimonious edge-colouring of graphs with maximum degree three
Jean-Luc Fouquet, Jean-Marie Vanherpe
In a graph of maximum degree 3, let denote the largest fraction of edges that can be 3 edge-coloured. Rizzi \cite{Riz09} showed that $γ(G) \geq 1-\frac{2\strut}{\strut 3…
On a family of cubic graphs containing the flower snarks
Jean-Luc Fouquet, Henri Thuillier, Jean-Marie Vanherpe
We consider cubic graphs formed with disjoint claws () such that for every integer modulo the three vertices of degree 1 o…