Lucas Pastor
Laboratoire G-SCOP, bureau B521
46 avenue Félix Viallet
38031 Grenoble Cedex 1

Telephone: +33 (0) 4 56 52 98 22

Lucas Pastor

I'm a second year PhD student in the Combinatorial Optimization team of G-SCOP. My advisors are Frédéric Maffray (G-SCOP) and Sylvain Gravier (Institut Fourier).
I'm working on graph theory. I am interested in about everything in this field even though my main works are about graph coloring and structural graph theory.



Disproving the normal graph conjecture

(with A. Harutyunyan and S. Thomassé)

A graph $G$ is called normal if there exist two coverings, $\mathbb{C}$ and $\mathbb{S}$ of its vertex set such that every member of $\mathbb{C}$ induces a clique in $G$, every member of $\mathbb{S}$ induces an independent set in $G$ and $C \cap S \neq \emptyset$ for every $C \in \mathbb{C}$ and $S \in \mathbb{S}$. It has been conjectured by De Simone and Körner in 1999 that a graph $G$ is normal if $G$ does not contain $C_5$, $C_7$ and $\overline{C_7}$ as an induced subgraph. We disprove this conjecture.

On the choosability of claw-free perfect graphs

(with Sylvain Gravier and Frédéric Maffray)

It has been conjectured that for every claw-free graph $G$ the choice number of $G$ is equal to its chromatic number. We focus on the special case of this conjecture where $G$ is perfect. Claw-free perfect graphs can be decomposed via clique-cutset into two special classes called elementary graphs and peculiar graphs. Based on this decomposition we prove that the conjecture holds true for every claw-free perfect graph with maximum clique size at most $4$.


The maximum weight stable set problem in ($P_6$, bull)-free graphs

(with Frédéric Maffray)
arXiv:1602.06817 $-$ Accepted in WG 2016

We present a polynomial-time algorithm that finds a maximum weight stable set in a graph that does not contain as an induced subgraph an induced path on six vertices or a bull (the graph with vertices $a, b, c, d, e$ and edges $ab, bc, cd, be, ce$).


$4$-coloring ($P_6$, bull)-free graphs

(with Frédéric Maffray)
arXiv:1511.08911 $-$ doi:10.1016/j.dam.2016.03.011

We present a polynomial-time algorithm that determines whether a graph that contains no induced path on six vertices and no bull (the graph with vertices $a,b,c,d,e$ and edges $ab,bc,cd,be,ce$) is $4$-colorable. We also show that for any fixed $k$ the $k$-coloring problem can be solved in polynomial time in the class of $(P_6,\mbox{bull},\mbox{gem})$-free graphs.


  • Séminaire LaBRI, équipe Graphes et Optimisation (Bordeaux, France) March 4 2016 The coloring problem in graphs with structural restrictions.

  • Séminaire G-SCOP (Grenoble, France) October 1st 2015 Coloration par liste dans les graphes parfaits sans griffe.

  • Third STINT meeting (Autrans, France) June 30 2015 List-coloring in claw-free perfect graphs.



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  • I'm a member of the ANR project STINT.
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