Maximal independent sets in caterpillar graphs

Authors:
Carmen Ortiz;MóNica Villanueva
Affiliations:
Faculty of Engineering and Science, Adolfo Ibáñez University, Chile;Faculty of Engineering, University of Santiago of Chile, Chile
Venue:
Discrete Applied Mathematics
Year:
2012

Citing 11
Cited 0

The number of maximal independent sets in a tree

SIAM Journal on Algebraic and Discrete Methods
The number of maximal independent sets in a connected graph

Discrete Mathematics
A note on independent sets in trees

SIAM Journal on Discrete Mathematics
The number of maximal independent sets in triangle-free graphs

SIAM Journal on Discrete Mathematics
Maximal independent sets in bipartite graphs

Journal of Graph Theory
Maximal independent sets in graphs with at most one cycle

Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
Object Recognition as Many-to-Many Feature Matching

International Journal of Computer Vision
Counting the number of independent sets in chordal graphs

Journal of Discrete Algorithms
Maximal independent sets in graphs with at most r cycles

Journal of Graph Theory
Maximal and maximum independent sets in graphs with at most r cycles

Journal of Graph Theory
The number of independent sets in unicyclic graphs

Discrete Applied Mathematics

Quantified Score

Hi-index	0.05

Visualization

Abstract

A caterpillar graph is a tree in which the removal of all pendant vertices results in a chordless path. In this work, we determine the number of maximal independent sets (mis) in caterpillar graphs. For a general graph, this problem is #P-complete. We provide a polynomial time algorithm to generate the whole family of mis in a caterpillar graph. We also characterize the independent graph (intersection graph of mis) and the clique graph (intersection graph of cliques) of complete caterpillar graphs.