Laminar Structure of Ptolemaic Graphs and Its Applications
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- 作者：Ryuhei Uehara ; Yushi Uno
- 关键词：algorithmic graph theory ; data structure ; Hamiltonian cycle ; intersection model ; ptolemaic graphs
- 刊名：Lecture Notes in Computer Science
- 出版时间：2005
- 出版年：2005
- 期刊代码：99_0302-9743
- 类别：cp
- 卷：3827
- 期：1
- 页码：pp.186-195
- 数据来源：sp
摘要
Ptolemaic graphs are graphs that satisfy the Ptolemaic inequality for any four vertices. The graph class coincides with the intersection of chordal graphs and distance hereditary graphs, and it is a natural generalization of block graphs (and hence trees). In this paper, a new characterization of ptolemaic graphs is presented. It is a laminar structure of cliques, and leads us to a canonical tree representation, which gives a simple intersection model for ptolemaic graphs. The tree representation is constructed in linear time from a perfect elimination ordering obtained by the lexicographic breadth first search. Hence the recognition and the graph isomorphism for ptolemaic graphs can be solved in linear time. Using the tree representation, we also give an O(n) time algorithm for the Hamiltonian cycle problem. Keywords: algorithmic graph theory, data structure, Hamiltonian cycle, intersection model, ptolemaic graphs.