A graph H is a square root of a graph G if two vertices are adjacent in G if and only if they are
at distance one or two in H. Computing a square root of a given graph is NP-hard, even …

Let D=(V (D), A (D)) be a digraph. The competition graph of D, is the graph with vertex set V
(D) and edge set {uv∈ V (D) 2:∃ w∈ V (D), uw⃗, vw⃗∈ A (D)}. The double competition …

In this paper we study the edge-clique cover number, θ e (⋅), of the tensor product K n× K n.
We derive an easy lowerbound for the edge-clique number of graphs in general. We prove …

For a graph G with vertices v1, v2,…, vn, a simple set representation of G is a family F={S1,
S2,…, Sn} of distinct nonempty sets such that| Si∩ Sj|= 1 if vivj is an edge in G, and| Si∩ …

A set of edges in a graph G is independent if no two elements are contained in a clique of G.
The edge-independent set problem asks for the maximal cardinality of independent sets of …

Let $ G $ be a graph with vertex set $ V (G) $ and edge set $ E (G) $. A family $\mathcal {S}
$ of nonempty sets $\{S_1,\ldots, S_n\} $ is a set representation of $ G $ if there exists a one …

We show that edge-clique graphs of cocktail party graphs have unbounded rankwidth. This,
and other observations lead us to conjecture that the edge-clique cover problem is NP …

The edge clique graph of a graph H is the one having the edge set of H as vertex set, two
vertices being adjacent if and only if the corresponding edges belong to a common complete …

A clique of a graph G is essential if it has an edge which does not belong to any other clique
in G. A graph G is weakly clique irreducible if every edge in G belongs to at least one …

Dört bölümden olu¸ san bu tezde Çizgelerin Sperner say¬ lar¬ tan¬ t¬ lm¬¸ s ve incelenmi¸
stir. Bu çal¬¸ smaya gerekli olan baz¬ temel Çizgeler teorisi ile ilgili tan¬ mlarla giri¸ s yap¬ …