Boundary cliques, clique trees and perfect sequences of maximal cliques of a chordal graph
Hisayuki Hara, Akimichi Takemura
Abstract
We characterize clique trees of a chordal graph in their relation to simplicial vertices and perfect sequences of maximal cliques. We investigate boundary cliques defined by Shibata and clarify their relation to endpoints of clique trees. Next we define a symmetric binary relation between the set of clique trees and the set of perfect sequences of maximal cliques. We describe the relation as a bipartite graph and prove that the bipartite graph is always connected. Lastly we consider to characterize chordal graphs from the aspect of non-uniqueness of clique trees.
Create a lesson
Related papers
The Project Scheduling Interdiction Problem with Delay Groups
Fei Wu, Erik Demeulemeester, Jannik Matuschke
Rank-Three Projections and Minimal Multiplicity Bipartitions of Path Complements
Jintao Fei, Jiangying Luo
Faster FPRAS for the Permanent via Restricted Poincaré Inequalities and Coupled Flows
Xiaoyu Chen, Eric Vigoda, Xiongxin Yang
On identifying codes on oriented graphs
Soura Sena Das, Sagnik Sen
Parallelizable Gradient-Based Optimization For Multi-Objective MaxCut
Jingjuan Huang, Alvaro Velasquez, Jia Liu et al.
Algebraic Characterizations for Minors of Finite Graphs via Flow Transformation Monoid Division and Embedding
Amena Assem, Hanna Derets, Chrystopher L. Nehaniv