Terminal backup, 3D matching, and covering cubic graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Terminal Backup, 3D Matching, and Covering Cubic Graphs
SIAM Journal on Computing
Packing paths: Recycling saves time
Discrete Applied Mathematics
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A k-piece of a graph G is a connected subgraph of G all of whose nodes have degree at most k and at least one node has degree equal to k. We consider the problem of covering the maximum number of nodes of a graph by node disjoint k-pieces. When k = 1 this is the maximum matching problem, and when k = 2 this is the problem, recently studied by Kaneko [19[, of covering the maximum number of nodes by disjoint paths of length greater than 1. We present a polynomial time algorithm for the problem as well as a Tutte-type existence theorem and a Berge-type min-max formula. We also solve the problem in the more general situation where the “pieces” are defined in terms of lower and upper bounds on the degrees. © 2006 Wiley Periodicals, Inc. J Graph Theory