## Salman Fawzi Ghazal

Associate professor
Mathematics department - Section I - Hadath
Speciality: Mathematics
Specific Speciality: Graph Theory

Positions
Teaching 4 Taught Courses
(2016-2017) M1102 - Algèbre 2 (for MIS students)

BS MISPCE (M: Mathematics, I: Computer Science, S: Statistics, P: Physics, C: Chemistry, E: Electronics)

(2016-2017) M1108 - Algèbre 4 (for PCE students)

BS MISPCE (M: Mathematics, I: Computer Science, S: Statistics, P: Physics, C: Chemistry, E: Electronics)

(2014-2015) Math 100 - Basics in Mathematics

BS Mathematics

(2014-2015) Math 103 - Linear Algebra II (Vector Space)

BS Mathematics

Education
2009 - 2011: Ph.D.

Lebanese University
Graph Theory

Very Honorable مع تهنئة اللجنة الفاحصة

2009 - 2011: Doctorat

Université Claude Bernard Lyon I
Graph Theory

Conferences 3 participations
ResearchInterests
Publications 6 publications
Salman Ghazal The structure of graphs with forbidden induced $C_4$, $\overline{C}_4$, $C_5$, $S_3$, chair and co-chair Electronic Journal of Graph Theory and Applications 2018

We find the structure of graphs that have no C4, $\overline{C}_4$, C5, S3, chair and co-chair as induced subgraphs. Then we deduce the structure of the graphs having no induced C4, $\overline{C_4}$, S3, chair and co-chair and the structure of the graphs G having no induced C4, $\overline{C_4}$ and such that every induced P4 of G is contained in an induced C5 of G.

Salman Ghazal New proofs of Konig's bipartite graph characterization theorem Indonesian Journal of Combinatorics 2017

We introduce four new elementary short proofs of the famous K\"{o}nig's theorem which characterizes bipartite graphs by absence of odd cycles. Our proofs are more elementary than earlier proofs because they use neither distances nor walks nor spanning trees.

Salman Ghazal About the second neighborhood problem in tournaments missing disjoint stars Electronic Journal of Graph Theory and Applications 2016

Let $D$ be a digraph without digons. Seymour's second neighborhood conjecture states that $D$ has a vertex $v$ such that $d^+(v) \leq d^{++}(v)$. Under some conditions, we prove this conjecture for digraphs missing $n$ disjoint stars. Weaker conditions are required when $n = 2$ or $3$. In some cases we exhibit two such vertices.

Salman Ghazal A Remark on the Second Neighborhood Problem Electronic Journal of Graph Theory and Applications 2015

Seymour’s second neighborhood conjecture states that every simple digraph (without digons) has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. Such a vertex is said to have the second neighborhood property (SNP). We define ”good” digraphs and prove a statement that implies that every feed vertex of a tournament has the SNP. In the case of digraphs missing a matching, we exhibit a feed vertex with the SNP by refining a proof due to Fidler and Yuster and using good digraphs. Moreover, in some cases we exhibit two vertices with SNP.

Salman Ghazal A Contribution to the Second Neighborhood Problem Springer 2013

Seymour’s Second Neighborhood Conjecture asserts that every oriented graph (without digons) has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. It is proved for tournaments, tournaments missing a matching and tournaments missing a generalized star. We prove this conjecture for classes of oriented graphs whose missing graph is a comb, a complete graph minus two independent edges, or a cycle of length 5.

Salman Ghazal Seymour's Second Neighborhood Conjecture for Tournaments Missing a Generalized Star John Wiley & Sons 2012

Seymour's Second Neighborhood Conjecture asserts that every digraph (without digons) has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. We prove its weighted version for tournaments missing a generalized star. As a consequence the weighted version holds for tournaments missing a sun, star, or a complete graph.

Languages
Arabic

Native or bilingual proficiency

English

Full professional proficiency

French

Professional working proficiency