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Questions about properties of and problems on graphs, discrete data structures that have the form of nodes connected by edges, that is networks.

1
vote
0answers
In a bipartite graph $(X+Y,E)$, it is possible to find a minimum vertex cover in polynomial time, by Konig's theorem. Suppose the minimum size is $s$. Is there an efficient algorithm for finding a ve …
asked Jan 20 by Erel Segal-Halevi
5
votes
1answer
I am looking for a reference for the following theorem: Let $G$ be a bipartite graph with partitions $X$ and $Y$, each with the same number of vertices ($n$). There is a nonempty subset $Y_1 \subset …
asked Dec 25 '13 by Erel Segal-Halevi
2
votes
1answer
An independent set is a set of vertices in a graph, no two of which are adjacent. A maximum independent set is a largest independent set for a given graph G. Is there a standard term for the size of …
asked Oct 30 '13 by Erel Segal-Halevi
5
votes
1answer
I am reading a unpublished paper describing an algorithm. In one step of the algorithm, there is a bipartite graph $G(X,Y,E)$, where $X=\{1,...,n\}$. For every subset $X' \subseteq X$, they define $ …
asked Dec 30 '13 by Erel Segal-Halevi
4
votes
1answer
What is a standard term for a matching in a bipartite graph, in which one part has less vertices than the other part, and the part with less vertices is fully matched (but the other part is, obviously …
asked Feb 1 '15 by Erel Segal-Halevi
7
votes
5answers
The government wants to create a team with one alchemist, one builder, and one computer-scientist. In order to have good cooperation, it is important that the 3 team-members like each other. There …
asked May 25 '13 by Erel Segal-Halevi
2
votes
2answers
There are $n$ people and $n$ items. For each person, there is a set of items he likes. Our goal is to give to each person a single item that he likes, i.e, find a perfect matching in the preference gr …
asked Apr 27 '18 by Erel Segal-Halevi
1
vote
0answers
Has the following version of the stable matching problem been studied? There are $k$ types of objects. There are $n$ producers, each of whom can produce a single object of any type, and has a …
asked Mar 1 '15 by Erel Segal-Halevi