Non-zero disjoint cycles in highly connected group labelled graphs

Authors:
Ken-ichi Kawarabayashi;Paul Wollan
Affiliations:
Graduate School of Information Sciences (GSIS), Tohoku University, Aramaki aza Aoba 09, Aoba-ku Sendai, Miyagi 980-8579, Japan;School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA
Venue:
Journal of Combinatorial Theory Series B
Year:
2006

Citing 3
Cited 7

Matroid minors

Handbook of combinatorics (vol. 1)
An improved linear edge bound for graph linkages

European Journal of Combinatorics - Special issue: Topological graph theory II
On Sufficient Degree Conditions for a Graph to be $k$-linked

Combinatorics, Probability and Computing

Approximating the list-chromatic number and the chromatic number in minor-closed and odd-minor-closed classes of graphs

Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On the connectivity of minimum and minimal counterexamples to Hadwiger's Conjecture

Journal of Combinatorial Theory Series B
A nearly linear time algorithm for the half integral parity disjoint paths packing problem

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Odd cycle packing

Proceedings of the forty-second ACM symposium on Theory of computing
Recognizing a totally odd K4-subdivision, parity 2-disjoint rooted paths and a parity cycle through specified elements

SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
FPT algorithms for path-transversal and cycle-transversal problems

Discrete Optimization
On group feedback vertex set parameterized by the size of the cutset

WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group @C. A cycle C in G has non-zero weight if for a given orientation of the cycle, when we add the labels of the forward directed edges and subtract the labels of the reverse directed edges, the total is non-zero. We are specifically interested in the maximum number of vertex disjoint non-zero cycles. We prove that if G is a @C-labelled graph and G@? is the corresponding undirected graph, then if G@? is 312k-connected, either G has k disjoint non-zero cycles or it has a vertex set Q of order at most 2k-2 such that G-Q has no non-zero cycles. The bound ''2k-2'' is best possible. This generalizes the results due to Thomassen (The Erdos-Posa property for odd cycles in graphs with large connectivity, Combinatorica 21 (2001) 321-333.), Rautenbach and Reed (The Erdos-Posa property for odd cycles in highly connected graphs, Combinatorica 21 (2001) 267-278.) and Kawarabayashi and Reed (Highly parity linked graphs, preprint.), respectively.