Homogeneously orderable graphs

Homogeneously Orderable Graphs

In this paper we introduce homogeneously orderable graphs which are a common generalization of distance-hereditary graphs, dually chordal graphs and homogeneous graphs. We present a characterization of the new class in terms of a tree structure of the closed neighborhoods of homogeneous sets in 2-graphs which is closely related to the defining elimination ordering. Moreover, we characterize the...

R-domination Problems on Homogeneously Orderable Graphs

In this paper, we consider r-dominating cliques in homogeneously orderable graphs (a common generalization of dually chordal and distance-hereditary graphs) and their relation to strict r-packing sets. We prove that a homogeneously orderable graph G possesses an r-dominating clique if and only if for any pair of vertices x , y of G d (x , y ) ° r ( x ) / r ( y ) / 1 holds where r : V r N is a g...

Collective Additive Tree Spanners of Homogeneously Orderable Graphs

In this paper we investigate the (collective) tree spanners problem in homogeneously orderable graphs. This class of graphs was introduced by A. Brandstädt et al. to generalize the dually chordal graphs and the distance-hereditary graphs and to show that the Steiner tree problem can still be solved in polynomial time on this more general class of graphs. In this paper, we demonstrate that every...

Properly orderable graphs

In a graph G = (V, E) provided with a linear order ”<” on V , a chordless path with vertices a, b, c, d and edges ab, bc, cd is called an obstruction if both a < b and d < c hold. Chvátal [2] defined the class of perfectly orderable graphs (i.e., graphs possessing an acyclic orientation of the edges such that no obstruction is induced) and proved that they are perfect. We introduce here the cla...

Uniquely Partially Orderable Graphs