TY - GEN

T1 - Smallest odd holes in claw-free graphs (extended abstract)

AU - Shrem, Shimon

AU - Stern, Michal

AU - Golumbic, Martin Charles

PY - 2010

Y1 - 2010

N2 - In this paper, we give general structure properties of a smallest odd hole in a claw-free graph that lead to a polynomial time algorithm. The algorithm is based on a modified BFS we call Γ-BFS. For a graph G with n vertices and m edges, the time complexity of the algorithm is O(nm 2). The algorithm is very easy to implement. We conclude the paper with a suggestion for an extension of our approach in order to detect an odd hole in a general graph.

AB - In this paper, we give general structure properties of a smallest odd hole in a claw-free graph that lead to a polynomial time algorithm. The algorithm is based on a modified BFS we call Γ-BFS. For a graph G with n vertices and m edges, the time complexity of the algorithm is O(nm 2). The algorithm is very easy to implement. We conclude the paper with a suggestion for an extension of our approach in order to detect an odd hole in a general graph.

KW - Claw-free graphs

KW - Holes

KW - Odd holes

KW - Polynomial time algorithms

KW - Triangle-free graphs

UR - http://www.scopus.com/inward/record.url?scp=72249123235&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-11409-0_29

DO - 10.1007/978-3-642-11409-0_29

M3 - Conference contribution

AN - SCOPUS:72249123235

SN - 3642114083

SN - 9783642114083

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 329

EP - 340

BT - Graph-Theoretic Concepts in Computer Science - 35th International Workshop, WG 2009, Revised Papers

T2 - 35th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2009

Y2 - 24 June 2009 through 26 June 2009

ER -