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We consider the complexity of approximation for the INDEPENDENT DOMINATING SET problem in 2P(3)-free graphs, i.e., graphs that do not contain two disjoint copies of the chordless path on three vertices as all induced subgraph. We show that, if P not equal ...
The graph coloring problem is one of the most famous problems in graph theory and has a large range of applications. It consists in coloring the vertices of an undirected graph with a given number of colors such that two adjacent vertices get different col ...
We consider the problem of finding in a graph a set R of edges to be colored in red so that there are maximum matchings having some prescribed numbers of red edges. For regular bipartite graphs with n nodes on each side, we give sufficient conditions f ...
It is a long standing open problem to find an explicit description of the stable set polytope of claw-free graphs. Yet more than 20 years after the discovery of a polynomial algorithm for the maximum stable set problem for claw-free graphs, there is even n ...
Graph theory is an important topic in discrete mathematics. It is particularly interesting because it has a wide range of applications. Among the main problems in graph theory, we shall mention the following ones: graph coloring and the Hamiltonian circuit ...
In this note we consider two coloring problems in mixed graphs, i.e., graphs containing edges and arcs. We show that they are both NP-complete in cubic planar bipartite graphs. This answers an open question from \cite{Ries2}. ...
This paper is motivated by a method used for DNA sequencing by hybridization presented in [Jacek Blazewicz, Marta Kasprzak, Computational complexity of isothernnic DNA sequencing by hybridization, Discrete Appl. Math. 154 (5) (2006) 718-7291. This paper pr ...
Steinhaus graphs on n vertices are certain simple graphs in bijective correspondence with binary {0,1}-sequences of length n-1. A conjecture of Dymacek in 1979 states that the only nontrivial regular Steinhaus graphs are those corresponding to the periodic ...
We consider the coloring problem for mixed graphs, that is, for graphs containing edges and arcs. A mixed coloring c is a coloring such that for every edge [xi,xj], c(xi)=c(xj) and for every arc (xp,xq), $c(x_{p})
