Séminaire d'équipe(s) Graphs, ALgorithms and Combinatorics

Locating pairs of vertices on Hamiltonian cycles
Hao Li

22 January 2016, 14:30 - 22 January 2016, 16:00 Salle/Bat : 235/PCRI-S
Contact :

Activités de recherche : Graph Theory

Résumé :

We first introduce some of our recent results that generalises Dirac's theorem in Hamiltonian graph theory. Then we will focus on the following conjecture of Enomoto that states that, if $G$ is a graph of order $n$ with minimum degree $delta(G)geq frac{n}{2}+1$, then for any pair of vertices $x$, $y$ in $G$, there is a Hamiltonian cycle $C$ of $G$ such that $d_C(x,y)=lfloor frac{n}{2}rfloor$. Weihua He, Qiang He and I gave a proof of Enomoto's conjecture for graphs of sufficiently large order. The main tools of our proof are Regularity Lemma of Szemer'{e}di and Blow-up Lemma of Koml'{o}s et al..