7 citations · 20 across the 23 of their papers we have counts for
10 papers · 1 filter
Totally Disjoint Diametral Paths
Tınaz Ekim, Arthur Farley
In this paper, we study totally disjoint diametral paths in simple connected graphs. A diametral path in a graph is a shortest path that connects two vertices whose mutual distance…
Sparse Sets in Triangle-free Graphs
Tınaz Ekim, Burak Nur Erdem, John Gimbel
A set of vertices is -sparse if it induces a graph with a maximum degree of at most . In this missive, we consider the order of the largest -sparse set in a triangle-free…
Constructing extremal triangle-free graphs using integer programming
Ali Erdem Banak, Tınaz Ekim, Z. Caner Taşkın
The maximum number of edges in a graph with matching number m and maximum degree d has been determined in [1] and [2], where some extremal graphs have also been provided. Then, a n…
Maximum size of a triangle-free graph with bounded maximum degree and matching number
Milad Ahanjideh, Tınaz Ekim, Mehmet Akif Yıldız
Determining the maximum number of edges under degree and matching number constraints have been solved for general graphs by Chvátal and Hanson (1976), and by Balachandran and Khare…
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…
Defective Ramsey Numbers and Defective Cocolorings in Some Subclasses of Perfect Graphs
Yunus Emre Demirci, Tınaz Ekim, Mehmet Akif Yıldız
In this paper, we investigate a variant of Ramsey numbers called defective Ramsey numbers where cliques and independent sets are generalized to -dense and -sparse sets, both…
Well-Totally-Dominated Graphs
Selim Bahadır, Tınaz Ekim, Didem Gözüpek
A subset of vertices in a graph is called a total dominating set if every vertex of the graph is adjacent to at least one vertex of this set. A total dominating set is called minim…
Defective Ramsey Numbers in Graph Classes
Yunus Emre Demirci, Tınaz Ekim, John Gimbel +1
Given a graph , a -sparse -set is a set of vertices inducing a subgraph with maximum degree at most . A -dense -set is a set of vertices that is -spars…
Mind the Independence Gap
Tınaz Ekim, Didem Gözüpek, Ademir Hujdurović +1
The independence gap of a graph was introduced by Ekim et al. (2018) as a measure of how far a graph is from being well-covered. It is defined as the difference between the maximum…
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…