Wenan Zang

An Approximation Algorithm for Feedback Vertex Sets in Tournaments

We obtain a necessary and sufficient condition in terms of forbidden structures for tournaments to possess the min-max relation on packing and covering directed cycles, together with strongly polynomial time algorithms for the feedback vertex set problem and the cycle packing problem in this class of tournaments. Applying the local ratio technique of Bar-Yehuda and Even to the forbidden structures, we find a 2.5-approximation polynomial time algorithm for the feedback vertex set problem in any tournament.

Hamilton paths in toroidal graphs

Tutte has shown that every 4-connected planar graph contains a Hamilton cycle. Grunbaum and Nash-Williams independently conjectured that the same is true for toroidal graphs. In this paper, we prove that every 4-connected toroidal graph contains a Hamilton path.

A TDI system and its application to approximation algorithms

We obtain a necessary and sufficient condition for tournaments to possess a min-max relation on packing and covering directed cycles, together with strongly polynomial time algorithms for the feedback vertex set problem and the cycle packing problem in this class of tournaments; the condition and the algorithms are all based on a totally dual integral (TDI) system, a theoretical framework introduced by J. Edmonds and R. Giles (1994) for establishing min-max results. As a consequence, we find a 2.5-approximation polynomial time algorithm for the feedback vertex set problem in any tournament.

Packing cycles in graphs, II

A graph G packs if for every induced subgraph H of G, the maximum number of vertex-disjoint cycles in H is equal to the minimum number of vertices whose deletion from H results in a forest. The purpose of this paper is to characterize all graphs that pack.

Approximating Longest Cycles in Graphs with Bounded Degrees

Jackson and Wormald conjecture that if

A Combinatorial Algorithm for Minimum Weighted Colorings of Claw-Free Perfect Graphs

G

Proof of Chv&tal's conjecture on maximal stable sets and maximal cliques in graphs

is a 3-connected

Corrigendum to proof of Chvátal's conjecture on maximal stable sets and maximal cliques in graphs

n

Proof of Toft's Conjecture: Every Graph Containing No Fully Odd K4 Is 3-Colorable

-vertex graph with maximum degree

Ramsey numbers involving large dense graphs and bipartite Turán numbers

d\ge 4