TY - GEN

T1 - Finding intersection models of weakly chordal graphs

AU - Golumbic, Martin Charles

AU - Lipshteyn, Marina

AU - Stern, Michal

PY - 2006

Y1 - 2006

N2 - We first present new structural properties of a two-pair in various graphs. A two-pair is used for characterizing weakly chordal graphs. Based on these properties, we prove the main theorem: a graph G is a weakly chordal (K 2,3, P6, 4P2, P2 ∪ P 4, H1, H1, H3)-bee graph if and only if G is an edge intersection graph of subtrees on a tree with maximum degree 4. This characterizes the so called [4, 4, 2] graphs. The proof of the theorem constructively finds the representation. Thus, we obtain a algorithm to construct an edge intersection model of subtrees on a tree with maximum degree 4 for such a given graph. This is a recognition algorithm for [4, 4, 2] graphs.

AB - We first present new structural properties of a two-pair in various graphs. A two-pair is used for characterizing weakly chordal graphs. Based on these properties, we prove the main theorem: a graph G is a weakly chordal (K 2,3, P6, 4P2, P2 ∪ P 4, H1, H1, H3)-bee graph if and only if G is an edge intersection graph of subtrees on a tree with maximum degree 4. This characterizes the so called [4, 4, 2] graphs. The proof of the theorem constructively finds the representation. Thus, we obtain a algorithm to construct an edge intersection model of subtrees on a tree with maximum degree 4 for such a given graph. This is a recognition algorithm for [4, 4, 2] graphs.

UR - http://www.scopus.com/inward/record.url?scp=33845535154&partnerID=8YFLogxK

U2 - 10.1007/11917496_22

DO - 10.1007/11917496_22

M3 - Conference contribution

AN - SCOPUS:33845535154

SN - 3540483810

SN - 9783540483816

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

SP - 241

EP - 255

BT - Graph-Theoretic Concepts in Computer Science - 32nd International Workshop, WG 2006, Revised Papers

PB - Springer Verlag

T2 - 32nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2006

Y2 - 22 June 2006 through 24 June 2006

ER -