Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
The monotone circuit complexity of Boolean functions
Combinatorica
A strengthening of Ben Rebea's lemma
Journal of Combinatorial Theory Series B
Finding and counting small induced subgraphs efficiently
Information Processing Letters
Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs
SIAM Journal on Computing
A Polynomial Algorithm for Recognizing Perfect Graphs
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Combinatorica
Journal of Graph Theory
Smallest Odd Holes in Claw-Free Graphs (Extended Abstract)
Graph-Theoretic Concepts in Computer Science
Claw-free graphs and two conjectures on omega, delta, and chi
Claw-free graphs and two conjectures on omega, delta, and chi
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A lemma of Fouquet implies that a claw-free graph contains an induced C"5, contains no odd hole, or is quasi-line. In this paper, we use this result to give an improved shortest-odd-hole algorithm for claw-free graphs by exploiting the structural relationship between line graphs and quasi-line graphs suggested by Chudnovsky and Seymour's structure theorem for quasi-line graphs. Our approach involves reducing the problem to that of finding a shortest odd cycle of length =5 in a graph. Our algorithm runs in O(m^2+n^2logn) time, improving upon Shrem, Stern, and Golumbic's recent O(nm^2) algorithm, which uses a local approach. The best known recognition algorithms for claw-free graphs run in O(m^1^.^6^9)@?O(n^3^.^5) time, or O(m^2)@?O(n^3^.^5) without fast matrix multiplication.