Questions tagged [bipartite-graphs]

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3
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90 views

Generating a random connected bipartite graph

A (n, m, k)-bipartite graph is a bipartite graphs with: independent sets of size $\{n, m\}$ a total of $k \geq n+m-1$ edges We want an algorithm to generate a (n, m, k)-bipartite selected uniformly ...
3
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0answers
235 views

Eigenvalues of adjacency matrix of a connected bipartite graph

Let $G=(V,E)$ is a connected d-regular bipartite graph with the same number of vertices on both sides of the bipartition. It's known that that the largest eigenvalue of its adjacency matrix would be d,...
3
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0answers
112 views

Is Permanent $+$-reducible?

Suppose we have two bipartite graphs $G_1$ and $G_2$ with perfect matching count $P_1$ and $P_2$ respectively then their disjoint union gives a bipartite graph with perfect matching $P_1P_2$. Is ...
2
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0answers
40 views

Counting matchings on 3-regular bipartite graphs

What I call a graph here allows parallel edges. Is the following problem #P-hard: INPUT: a 3-regular bipartite graph $G$ OUTPUT: the number of matchings of $G$. It is known that counting matchings ...
2
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0answers
54 views

Degree distribution of certain subgraphs of a biregular graph

Consider a bipartite graph $G=(X,Y)$, such that the degree of a left node $x \in X$ is $l$, and the degree of a right node $y \in Y$ is $r$. The number of edges is $|E|=|X|l=|Y|r$. Pick $w$ nodes in ...
1
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0answers
104 views

algorithms for a large submatrix / general factor / quasi-biclique problem?

Given a sparse 0/1 matrix $X$, too large to fit in memory, with $m$ rows and $n$ columns, I'm looking for an algorithm for finding a submatrix (when one exists) with maximum number of rows such that ...
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0answers
90 views

Algorithm for maximum bipartite matching with arriving edges?

Given a bipartite graph with fixed nodes and incrementally arriving edges, is there any efficient algorithm to compute and update the maximum matching?
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5 views

Integral maxflow with on or off constraint?

I have a graph (bipartite) on which I want to do max flow (each edge $e$ has capacity $r_e$) and so I can obtain polynomial time algorithm by capacity scaling results. I also have the additional ...
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0answers
80 views

Does simplex algorithm run in polynomial on Bipartite Perfect matching polytope?

It is well known that simplex algorithm runs in exponential time in worst case. However are there situations (necessary and sufficient conditions) where simplex algorithm runs in polynomial time? In ...
0
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0answers
28 views

Alternating Delivery Problem

What is known about the complexity of the following problem: Suppose we have a complete bipartite graph $G(V,E)$ with disjoint sets $C$ and $T$. The candidate vertices, and the target vertices ...