8 papers
An improved bound for 2-distance coloring of planar graphs with girth six
Zakir Deniz
A vertex coloring of a graph is said to be a 2-distance coloring if any two vertices at distance at most from each other receive different colors, and the least number of c…
Critical Equimatchable Graphs
Zakir Deniz, Tınaz Ekim
A graph G is equimatchable if every maximal matching of G has the same cardinality. In this paper, we investigate equimatchable graphs such that the removal of any edge harms the e…
Sectionable Tournaments: Their topology and Coloring
Zakir Deniz
We provide a detailed study of topological and combinatorial properties of sectionable tournaments. This class forms an inductively constructed family of tournaments grounded over…
Order-sensitive domination in partially ordered sets
Yusuf Civan, Zakir Deniz, Mehmet Akif Yetim
For a (finite) partially ordered set (poset) , we call a dominating set in the comparability graph of , an order-sensitive dominating set in if either or els…
On graphs admitting two disjoint maximum independent sets
Zakir Deniz, Vadim E. Levit, Eugen Mandrescu
An independent set A is maximal if it is not a proper subset of an independent set, while A is maximum if it has a maximum size. The problem of whether a graph has a pair of disjoi…
On contact graphs of paths on a grid
Zakir Deniz, Esther Galby, Andrea Munaro +1
In this paper we consider Contact graphs of Paths on a Grid (CPG graphs), i.e. graphs for which there exists a family of interiorly disjoint paths on a grid in one-to-one correspon…
On two extensions of equimatchable graphs
Zakir Deniz, Tınaz Ekim, Tatiana Romina Hartinger +2
A graph is said to be equimatchable if all its maximal matchings are of the same size. In this work we introduce two extensions of the property of equimatchability by defining two…
Edge-Stable Equimatchable Graphs
Zakir Deniz, Tınaz Ekim
A graph is \emph{equimatchable} if every maximal matching of has the same cardinality. We are interested in equimatchable graphs such that the removal of any edge from the…