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20192026

most citedDefective Ramsey Numbers in Graph Classes

2 citations · 4 across the 10 of their papers we have counts for

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8 papers · 1 filter

math.CO2024

Path decompositions of oriented graphs

Viresh Patel, Mehmet Akif Yıldız

We consider the problem of decomposing the edges of a digraph into as few paths as possible. A natural lower bound for the number of paths in any path decomposition of a digraph $D…

math.CO2023

Cycle Partitions in Dense Regular Digraphs and Oriented Graphs

Allan Lo, Viresh Patel, Mehmet Akif Yıldız

A conjecture of Jackson from 1981 states that every $d$ -regular oriented graph on $n$ vertices with $n \leq 4 d + 1$ is Hamiltonian. We prove this conjecture for sufficiently large $n$ …

math.CO2022★ 1 cited

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…

math.CO2022

Hamilton Cycles in Dense Regular Digraphs and Oriented Graphs

Allan Lo, Viresh Patel, Mehmet Akif Yıldız

We prove that for every $ε > 0$ there exists $n_{0} = n_{0} (ε)$ such that every regular oriented graph on $n > n_{0}$ vertices and degree at least $(1/4 + \varepsilon)n…

math.CO2021

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 $k$ -dense and $k$ -sparse sets, both…

math.CO2019★ 2 cited

Defective Ramsey Numbers in Graph Classes

Yunus Emre Demirci, Tınaz Ekim, John Gimbel +1

Given a graph $G$ , a $k$ -sparse $j$ -set is a set of $j$ vertices inducing a subgraph with maximum degree at most $k$ . A $k$ -dense $i$ -set is a set of $i$ vertices that is $k$ -spars…

math.CO2019

Linear Time Recognition of Equimatchable Split Graphs

Mehmet Akif Yıldız

A maximal matching $M$ that consists of independent edges is a subgraph of a simple and undirected graph $G$ for which $G - M$ forms an independent set. A graph $G$ is called equimat…

math.CO2019★ 1 cited

A study on random permutation graphs

Oğuz Gürerk, Ümit Işlak, Mehmet Akif Yıldız

For a given permutation $π_{n}$ in $S_{n}$ , a random permutation graph is formed by including an edge between two vertices $i$ and $j$ if and only if $(i - j) (π_{n} (i) - π_{n} (j)) < 0$ .…