Algorithm Theory , Winter Term 2015 / 16 Problem Set 9 - Sample Solution Exercise 1 : Maximum Matching ( 6 points )
نویسنده
چکیده
We are given a bipartite graph B = (U ∪̇V, E) on two disjoint node sets U and V ; each edge connects a node in U to a node in V . In the following, we define a 2-claw to be a set of three distinct nodes {u, x, y} such that u ∈ U , x, y ∈ V and there is an edge from u to both nodes x and y. We consider the following maximization problem on the graph B: Find a largest possible set of vertexdisjoint set of 2-claws. In other words, we want to find a largest possible subset of edges such that every node in U is incident to either 0 or 2 of the edges and each node in V is incident to either 0 or 1 of the edges (i.e., each node is either part of one 2-claw or it is not part of any 2-claw at all).
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