Let denote a set of additive hereditary graph properties. It is a known fact that a partially ordered set is a complete distributive lattice. We present results when a join of two additive hereditary graph properties in has a finite or infinite family of minimal forbidden subgraphs.
B-products of graphs and their generalizations were introduced in [4]. We determined the parameters k, l of (k,l)-kernels in generalized B-products of graphs. These results are generalizations of theorems from [2].
Let ⁿ be a given set of unlabeled simple graphs of order n. A maximal common subgraph of the graphs of the set ⁿ is a common subgraph F of order n of each member of ⁿ, that is not properly contained in any larger common subgraph of each member of ⁿ. By well-known Dirac’s Theorem, the Dirac’s family ⁿ of the graphs of order n and minimum degree δ ≥ [n/2] has a maximal common subgraph containing Cₙ. In this note we study the problem of determining all maximal common subgraphs of the Dirac’s family...
A unit disk graph is the intersection graph of a family of unit disks in the plane. If the disks do not overlap, it is also a unit coin graph or penny graph. It is known that finding a maximum independent set in a unit disk graph is a NP-hard problem. In this work we extend this result to penny graphs. Furthermore, we prove that finding a minimum clique partition in a penny graph is also NP-hard, and present two linear-time approximation algorithms for the computation of clique partitions: a 3-approximation...
A unit disk graph is the intersection graph of a family of unit disks in the plane. If the disks do not overlap, it is also a unit coin graph or penny graph. It is known that finding a maximum independent set in a unit disk graph is a NP-hard problem. In this work we extend this result to penny graphs. Furthermore, we prove that finding a minimum clique partition in a penny graph is also NP-hard, and present two linear-time approximation algorithms for the computation of clique partitions: a 3-approximation...
We study domination between different types of walks connecting two non-adjacent vertices u and v of a graph (shortest paths, induced paths, paths, tolled walks). We succeeded in characterizing those graphs in which every uv-walk of one particular kind dominates every uv-walk of other specific kind. We thereby obtained new characterizations of standard graph classes like chordal, interval and superfragile graphs.
Strongly perfect graphs were introduced by C. Berge and P. Duchet in [1]. In [4], [3] the following was studied: the problem of strong perfectness for the Cartesian product, the tensor product, the symmetrical difference of n, n ≥ 2, graphs and for the generalized Cartesian product of graphs. Co-strong perfectness was first studied by G. Ravindra andD. Basavayya [5]. In this paper we discuss strong perfectness and co-strong perfectness for the generalized composition (the lexicographic product)...