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Questions tagged [vertex-cover]

28 questions
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A set of vertices is a vertex cover if and only if its complement is an independent set

This following property is from wiki vertex cover: A set of vertices is a vertex cover if and only if its complement is an independent set. I was wondering how do we prove that this is true? It would be great if it can be proved by contradiction but…
liketolearn
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Vertex cover for tree greedy approach

Question: Let T be an n-node tree rooted at some node r. We want to place as few guards as possible on nodes of T, such that every edge of T is guarded: an edge between a parent node v and its child w is guarded if one places a guard on at least one…
Howard Wang
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cardinality vertex cover with maximum matching in polynomial time

Is the problem of cardinality vertex cover solvable using the maximum matching in polynomial time? What is the coefficient of approximation? please help me
hagard
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A graph, G, has a minimum vertex cover of size |V| - 1 if and only if G is complete. Is it true?

A mesh can be an example of a complete G. Where each node is connected to every other node. So shouldn't the minimum vertex cover size for such a graph is '1'.
Tushar
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Not able to understand this graph property

I read that in a simple graph, |minimal vertex cover| <= 2*|maximal matching|. Consider a graph show here:- Here a minimal vertex cover can be {B,C,D,E} which has a size of 4 and size of maximal matching is just 1. So, 4>2*1 and the property…
Zephyr
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Minimum vertex cover

I am trying to get a vertex cover for an "almost" tree with 50,000 vertices. The graph is generated as a tree with random edges added in making it "almost" a tree. I used the approximation method where you marry two vertices, add them to the…
Ccyan
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Non-Deterministic Algorithm for Vertex Cover

I had a problem in my class quiz to write a non determinstic algorithm for Vertex Cover. We discussed about the solution with our instructor and he told that the level indeterminancy should not be too high. It should be sensibly good. I am confused…
Laschet Jain
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How do I prove the correctness of my greedy algorithm for vertex cover on a tree?

The vertex cover problem on trees is as follows. Input: an acyclic simple undirected graph G Output: a set of vertices W such that, for every edge uv, u ∈ W or v ∈ W. We want to minimize the size of W. My greedy algorithm is to initialize W =…
Rumen Hristov
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Which algorithm is best appropriate for finding Vertex Cover over large graphs using parallel approach?

There are lots of algorithm for finding vertex cover of a graph but want to know the best algorithm that can be used as parallel approach for finding vertex cover over large graph, so which is best? As i have asked this question bcoz the importance…
Smit Patel
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How to perform a relaxation of an integer linear programming formulation of graph vertex cover?

I'm implementing the optimization algorithms from Kernelization Algorithms for the Vertex Cover Problem: Theory and Experiments (PDF). I'm a bit stuck at chapter 2.3: Kernelization by linear programming. The idea of this technique (in ILP…
helluin
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How to convert SPOJ Quest4 to Minimum Vertex Cover

The following is a Maximum Bipartite matching problem : http://www.spoj.com/problems/QUEST4/ Through forums i came to know that the problem can be converted into a Minimum Vertex Cover problem, which in turn can be solved by Maximum Bipartite…
rohitjv
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Covering k edges with minimum number of vertices

I am trying to write a DP algorithm that calculates the minimum number of vertices we need to select in order to cover k edges on a graph. The code I have written so far…
user12610369
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Prove that any minimum vertex cover of a clique of size n must have exactly n-1 vertices

How to prove that any minimum vertex cover of a clique of size n must have exactly n-1 vertices? THx
user3047166
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