On some special classes of contact B0-VPG graphs

On Some Special Classes of Sonnenschein Matrices

‎In this paper we consider the special classes of Sonnenschein matrices‎, ‎namely the Karamata matrices $K[alpha,beta]=left(a_{n,k}right)$ with the entries‎ ‎[{a_{n,k}} = sumlimits_{v = 0}^k {left( begin{array}{l}‎ ‎n\‎ ‎v‎ ‎end{array} right){{left( {1‎ - ‎alpha‎ - ‎beta } right)}^v}{alpha ^{n‎ - ‎v}}left( begin{array}{l}‎ ‎n‎ + ‎k‎ - ‎v‎ - ‎1\‎ ‎,,,,,,,,,,k...

Reed's conjecture on some special classes of graphs

Reed conjectured that for any graph G, χ(G) ≤ ⌈ ω(G)+∆(G)+1 2 ⌉, where χ(G), ω(G), and ∆(G) respectively denote the chromatic number, the clique number and the maximum degree of G. In this paper, we verify this conjecture for some special classes of graphs, in particular for subclasses of P5-free graphs or Chair-free graphs.

α Valuations of Special Classes of Quadratic Graphs

Gamma Graphs of Some Special Classes of Trees

A set S ⊂ V is a dominating set of a graph G = (V,E) if every vertex v ∈ V which does not belong to S has a neighbour in S. The domination number γ(G) of the graph G is the minimum cardinality of a dominating set in G. A dominating set S is a γ-set in G if |S| = γ(G). Some graphs have exponentially many γ-sets, hence it is worth to ask a question if a γ-set can be obtained by some transformatio...

Selective Graph Coloring in Some Special Classes of Graphs

In this paper, we consider the selective graph coloring problem. Given an integer k ≥ 1 and a graph G = (V,E) with a partition V1, . . . , Vp of V , it consists in deciding whether there exists a set V ∗ in G such that |V ∗ ∩ Vi| = 1 for all i ∈ {1, . . . , p}, and such that the graph induced by V ∗ is k-colorable. We investigate the complexity status of this problem in various classes of graphs.