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Graduate
By
Shiva Kintali
on Sept. 11, 2012 | Updated Dec. 6, 2017
Vertex cover in bipartite graphs
The Vertex Cover of a graph \(G(V,E)\) is a set of vertices \(S \subseteq V\) such that each edge of the graph is incident to at least one vertex of the set \(S\). Minimum cost vertex cover : Given a…
Mathematics
Optimization
Graph Theory
Linear Programming
bipartite graph
vertex cover
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Graduate
By
Shiva Kintali
on June 9, 2012 | Updated Dec. 6, 2017
Minimum edge cover vs Maximum matching
An edge cover of a graph \(G(V,E)\) is a subset \(F \subseteq E\) of edges such that every node is incident to at least one edge in \(F\). Show that a minimum cardinality edge cover can be determine…
Mathematics
Optimization
Graph Theory
Linear Programming
edge cover
matching
reduction
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Graduate
By
Shiva Kintali
on June 6, 2012 | Updated Dec. 6, 2017
Perfect Matchings in Cubic Graphs
Let \(G\) be a cubic graph with no cut-edge. Let \(PM(G)\) be the convex hull of the perfect matchings of \(G\). Prove that the vector \((1/3, 1/3, \dots, 1/3) \in PM(G)\). Prove that every two-conn…
Mathematics
Optimization
Combinatorial Optimization
Graph Theory
matching
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Undergraduate
By
Shiva Kintali
on June 9, 2012 | Updated Dec. 6, 2017
Linear inequalities satisfied with equality
Let \(Ax \leq b\) be a system of linear inequalities. Describe a linear program to determine which inequalities among \(Ax \leq b\) are always satisfied with equality.
Optimization
Linear Programming
optimization
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