Claw-free graphs. V. Global structure

Authors:
Maria Chudnovsky;Paul Seymour
Affiliations:
Columbia University, New York, NY 10027, USA;Princeton University, Princeton, NJ 08544, USA
Venue:
Journal of Combinatorial Theory Series B
Year:
2008

Citing 4
Cited 15

Claw-free graphs. I. Orientable prismatic graphs

Journal of Combinatorial Theory Series B
Claw-free graphs. II. Non-orientable prismatic graphs

Journal of Combinatorial Theory Series B
Claw-free graphs. III. Circular interval graphs

Journal of Combinatorial Theory Series B
Claw-free graphs. IV. Decomposition theorem

Journal of Combinatorial Theory Series B

Claw-free graphs VI. Colouring

Journal of Combinatorial Theory Series B
Independent Sets of Maximum Weight in Apple-Free Graphs

SIAM Journal on Discrete Mathematics
Domination when the stars are out

ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Claw-free graphs with strongly perfect complements. Fractional and integral version. Part I. Basic graphs

Discrete Applied Mathematics
Claw-free graphs with strongly perfect complements. Fractional and integral version, Part II: Nontrivial strip-structures

Discrete Applied Mathematics
Dominating set is fixed parameter tractable in claw-free graphs

Theoretical Computer Science
Clique minors in claw-free graphs

Journal of Combinatorial Theory Series B
The structure of bull-free graphs I-Three-edge-paths with centers and anticenters

Journal of Combinatorial Theory Series B
Complete Minors and Independence Number

SIAM Journal on Discrete Mathematics
An algorithmic decomposition of claw-free graphs leading to an O(n3)-algorithm for the weighted stable set problem

Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A fast algorithm to remove proper and homogeneous pairs of cliques (while preserving some graph invariants)

Operations Research Letters
A proof of a conjecture on diameter 2-critical graphs whose complements are claw-free

Discrete Optimization
Claw-free graphs. VII. Quasi-line graphs

Journal of Combinatorial Theory Series B
Triangulation and clique separator decomposition of claw-free graphs

WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
2-clique-bond of stable set polyhedra

Discrete Applied Mathematics

Quantified Score

Hi-index	0.01

Visualization

Abstract

A graph is claw-free if no vertex has three pairwise nonadjacent neighbours. In earlier papers of this series we proved that every claw-free graph either belongs to one of several basic classes that we described explicitly, or admits one of a few kinds of decomposition. In this paper we convert this ''decomposition'' theorem into a theorem describing the global structure of claw-free graphs.