Data structures and network algorithms
Data structures and network algorithms
Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
Finding approximate separators and computing tree width quickly
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Decision algorithms for unsplittable flow and the half-disjoint paths problem
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Highly connected sets and the excluded grid theorem
Journal of Combinatorial Theory Series B
The extremal function for complete minors
Journal of Combinatorial Theory Series B
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization
Journal of Computer and System Sciences
Packing Non-Zero A-Paths In Group-Labelled Graphs
Combinatorica
A nearly linear time algorithm for the half integral disjoint paths packing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Planar graph bipartization in linear time
Discrete Applied Mathematics
Some remarks on the odd hadwiger’s conjecture
Combinatorica
On the odd-minor variant of Hadwiger's conjecture
Journal of Combinatorial Theory Series B
Linear connectivity forces large complete bipartite minors
Journal of Combinatorial Theory Series B
Combinatorica
Finding odd cycle transversals
Operations Research Letters
Proceedings of the forty-second ACM symposium on Theory of computing
Compression via matroids: a randomized polynomial kernel for odd cycle transversal
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Contracting graphs to paths and trees
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
On polynomial kernels for structural parameterizations of odd cycle transversal
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Parameterized tractability of multiway cut with parity constraints
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Finding small separators in linear time via treewidth reduction
ACM Transactions on Algorithms (TALG)
A faster FPT algorithm for Bipartite Contraction
Information Processing Letters
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We consider the following problem, which is called the odd cycles transversal problem. Input: A graph G and an integer k. Output: A vertex set X ∈ V(G) with |X| ≤ k such that G -- X is bipartite. We present an O(mα(m, n)) time algorithm for this problem for any fixed k, where n, m are the number of vertices and the number of edges, respectively, and the function α(m, n) is the inverse of the Ackermann function (see by Tarjan [38]). This improves the time complexity of the algorithm by Reed, Smith and Vetta [29] who gave an O(nm) time algorithm for this problem. Our algorithm also implies the edge version of the problem, i.e, there is an edge set X' ε E(G) such that G -- X' is bipartite. Using this algorithm and the recent result in [16], we give an O(mα(m, n) + n log n) algorithm for the following problem for any fixed k: Input: A graph G and an integer k. Output: Determine whether or not there is a half-integral k disjoint odd cycles packing, i.e, k odd cycles C1,..., Ck in G such that each vertex is on at most two of these odd cycles. This improves the time complexity of the algorithm by Reed, Smith and Vetta [29] who gave an O(n3) time algorithm for this problem. We also give a much simpler and much shorter proof for the following result by Reed [28]. The Erdős-Pósa property holds for the half-integral disjoint odd cycles packing problem. I.e. either G has a half-integral k disjoint odd cycles packing or G has a vertex set X of order at most f (k) such that G -- X is bipartite for some function f of k. Note that the Erdős-Pósa property does not hold for odd cycles in general.