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We present an algorithm for the vertex cover problem by combining the LP relaxation and the random edge-reductions. The algorithm has the expected approximation ratio of 1.344.
In this work, we mainly investigate the problem that minimizes the price function such that the valuation function exceeds a required threshold in submodular cover problem, where the price function is...
We provide conditions that classify cover times for sequences of random walks on random graphs into two types: One type (type 1) is the class of cover times approximated by the maximal hitting times s...
Abstract: Let $M$ be a module. A {\em $\delta$-cover} of $M$ is an epimorphism from a module $F$ onto $M$ with a $\delta$-small kernel. A $\delta$-cover is said to be a {\em flat $\delta$-cover} in ca...
We prove the relation between the Hodge structure of the double cover of a nonsingular cubic surface branched along its Hessian and the Hodge structure of the triple cover of P3 branched along the cub...
A subset S of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from S. Denote by k(G)the minimum cardinality of a k-path vertex cover i...
It was shown in my earlier article that the splice diagram of a rational homology sphere graph manifold determines the manifolds universal abelian cover. In this article we use the proof of this to g...
Given a rational homology sphere M, whose splice diagram satisfy the semigroup condition, Neumann and Wahl were able to define a complete intersection surface singularity called splice diagram singul...
We show that the probability that a simple random walk covers a finite, bounded degree graph in linear time is exponentially small. More precisely, for every D and C, there exists a=a(D,C)>0 such t...
Given a link in the three-sphere, Z. Szab\'o and the second author constructed a spectral sequence starting at the Khovanov homology of the link and converging to the Heegaard Floer homology of its br...
We study compact Kähler threefolds X with infinite fundamental group whose universal cover can be compactified. Combining techniques from L2-theory, Campana’s geometric orbifolds and the minimal ...
It is well known that a graph with m edges can be made triangle-free by removing (slightly less than) m/2 edges. On the other hand, there are many classes of graphs which are hard to make triangle-f...
For an arbitrary non-empty closed convex set $A$ in $\mathbb{R}^n$, we prove that the polar of the difference between the barrier cone $\mathbb{B}(A)$ and its interior $\text{int } \mathbb{B} (A)$ co...
Let R be a commutative ring with identity and M be an R-module with Spec(M) \neq f. A cover of the R-submodule K of M is a subset C of Spec(M) satisfying that for any x \in K, x \neq 0, there is N \in...

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