Selected papers from the second Krakow conference on Graph theory
On a closure concept in claw-free graphs
Journal of Combinatorial Theory Series B
Pancyclicity and NP-completeness in planar graphs
Discrete Applied Mathematics
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Computing the Tutte Polynomial in Vertex-Exponential Time
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Finding, minimizing, and counting weighted subgraphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Computing sharp 2-factors in claw-free graphs
Journal of Discrete Algorithms
Counting perfect matchings as fast as Ryser
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
| Hi-index | 0.89 |
A closed trail is a connected graph whose every vertex is incident to an even number of edges. We give a deterministic algorithm that in time 2^m^/^2poly(m,n) finds the number of closed trails in a given graph G with n vertices and m edges. Moreover, within the same time bound we can determine every possible vertex set of a closed trail in G, together with the associated number of closed trails. Our algorithm can be used to deterministically find the longest cycle in an n-vertex claw-free graph in time 2^n^/^2poly(m,n) via a framework presented by Broersma et al. (in press, http://dx.doi.org/10.1007/s00453-011-9576-4) [5], thus improving both upon the O(1.66^n) time randomized algorithm for general graphs (Bjorklund, 2010, http://dx.doi.org/10.1109/FOCS.2010.24, [1]), as well as the O(1.69^n) time deterministic algorithm for claw-free graphs by Broersma et al.