Recognizing Graphs without Asteroidal Triples

Authors:
Ekkehard Köhler
Affiliations:
-
Venue:
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
Year:
2000

Citing 6
Cited 0

Triangulating graphs without asteroidal triples

Discrete Applied Mathematics
Linear time algorithms for graph search and connectivity determination on complement graphs

Information Processing Letters
Linear Time Algorithms for Dominating Pairs in Asteroidal Triple-free Graphs

SIAM Journal on Computing
The ultimate interval graph recognition algorithm?

Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
On Claw-Free Asteroidal Triple-Free Graphs

WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms

Journal of Computer and System Sciences

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the problem of recognizing AT-free graphs. Although there is a simple O(n3) algorithm, no faster method for solving this problem had been known. Here we give three different algorithms which have a better time complexity for graphs which are sparse or have a sparse complement; in particular we give algorithms which recognize AT-free graphs in O(nm + n2), O(m3/2 + n2), and O(n2.82 + nm). In addition we give a new characterization of graphs with bounded asteroidal number by the help of the knotting graph, a combinatorial structure which was introduced by Gallai for considering comparability graphs.