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 -