‎in this paper‎, ‎we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is cohen-macaulay‎. ‎it is proved that if there exists a cover of an $r$-partite cohen-macaulay graph by disjoint cliques of size $r$‎, ‎then such a cover is unique‎.

Every 2-connected simple cubic graph of order n¿ 6 has a cycle cover with at most n=4 cycles. This bound is best possible. c © 2003 Elsevier B.V. All rights reserved.

A cycle cover of a graph G is a collection of disjoint cycles that spans G. Generally, a (possibly disconnected) cycle cover is easier to construct than a connected (Hamiltonian) cycle cover. One might expect this since the cycle cover property is local whereas connectivity is a global constraint. We compare the hardness of CONNECTED CYCLE COVER and CYCLE COVER under various constraints (both l...

Multi-channel, high throughput experimental methodologies for flow cytometry are transforming clinical immunology and hematology, and require the development of algorithms to analyze the highdimensional, large-scale data. We describe the development of two combinatorial algorithms to identify rare cell populations in data from mice with acute promyelocytic leukemia. The flow cytometry data is c...

This paper explains the important conceptual and technical differences between the method of p-cycles and two other recent advances involving a cyclic orientation to protection. These are enhanced rings and cycle double covers. The most fundamental difference that is unique to p-cycles is the aspect of straddling span failure protection. This enables mesh-like efficiency levels at well under 10...

Let H = (H; V) be a hypergraph with edge set H and vertex set V. Then H is invertible ii there exists a permutation of V such that for all E 2 H, (E) \ E = ;. H is invertibility critical if H is not invertible but every hypergraph obtained by removing an edge from H is invertible. The degree of H is d if fE 2 Hjx 2 Eg d for each x 2 V. Let i(d) be the maximum number of edges of an invertibility...

To achieve fast link failure detection in all-optical networks, the notion of monitoring-cycle (m-cycle) is introduced. The best known m-cycle construction algorithm (HST [7]) adopts a spanning tree-based approach. In this paper, we propose a new algorithm M-CYCLE to construct a set of minimum-length mcycles (or m-cycles) for more efficient link failure detection. We prove that the performance ...

In the vertex cover problem we are given a graph G = (V,E) and an integer k and have to determine whether there is a set X ⊆ V of size at most k such that each edge in E has at least one endpoint in X. The problem can be easily solved in time O∗(2k), making it fixed-parameter tractable (FPT) with respect to k. While the fastest known algorithm takes only time O∗(1.2738k), much stronger improvem...

In a typical covering problem we are given a universe U of size n, a family S (S could be given implicitly) of sizem and an integer k and the objective is to check whether there exists a subfamily S ′ ⊆ S of size at most k satisfying some desired properties. If S ′ is required to contain all the elements of U then it corresponds to the classical Set Cover problem. On the other hand if we requir...

The cover time of a graph is a celebrated example of a parameter that is easy to approximate using a randomized algorithm, but for which no constant factor deterministic polynomial time approximation is known. A breakthrough due to Kahn, Kim, Lovász and Vu [23] yielded a (log log n) polynomial time approximation. We refine the upper bound of [23], and show that the resulting bound is sharp and ...