Convexity and HHD-Free Graphs

Authors:
Feodor F. Dragan;Falk Nicolai;Andreas Brandstädt
Affiliations:
-;-;-
Venue:
SIAM Journal on Discrete Mathematics
Year:
1999

Citing 0
Cited 8

Finding a central vertex in an HHD-free graph

Discrete Applied Mathematics - Special issue: The second international colloquium, "journées de l'informatique messine"
Oracles for vertex elimination orderings

Theoretical Computer Science
Steiner distance and convexity in graphs

European Journal of Combinatorics
Local Steiner convexity

European Journal of Combinatorics
Finding a central vertex in an HHD-free graph

Discrete Applied Mathematics
The induced path function, monotonicity and betweenness

Discrete Applied Mathematics
On the contour of graphs

Discrete Applied Mathematics
On the Carathéodory number of interval and graph convexities

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

It is well known that chordal graphs can be characterized via m-convexity. In this paper we introduce the notion of m3-convexity (a relaxation of m-convexity) which is closely related to semisimplicial ordering of graphs. We present new characterizations of HHD-free graphs via m3-convexity and obtain some results known from [B. Jamison and S. Olariu, Adv. Appl. Math., 9 (1988), pp. 364--376] as corollaries. Moreover, we characterize weak bipolarizable graphs as the graphs for which the family of all m3-convex sets is a convex geometry. As an application of our results we present a simple efficient criterion for deciding whether a HHD-free graph contains a r-dominating clique with respect to a given vertex radius function r.