Applied and Algorithmic Graph Theory
Designed as a bridge to cross the gap between mathematics and computer science, and planned as the mathematics base for computer science students, this maths text is designed to help the student develop an understanding of the concept of an efficient algorithm.
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An Introduction to Algorithms
Paths and Distance in Graphs
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1-factor active vertex adjacency list alternating tree apply assigned Assume augmenting path belongs bipartite graph breadth-first search color complete graph complexity of Step component of G connected graph construct Corollary corresponding cut-vertex degree sequence deleted denote depth-first search dfi(v digraph edge of G edges incident efficient algorithm embedding end-vertex eulerian circuit example exists follows G contains G of Figure G of order given graph graph G graph of order Graph Theory hamiltonian cycle Hence induced isomorphic labeled Let G maximum flow maximum matching maximum number maximum weight minimum spanning tree multigraph nontrivial NP-complete obtained otherwise pair PARENT(v partite sets path in G Petersen graph planar graph plane positive integer Problem Set produces Proof Ramsey numbers return to Step rooted tree semipath shortest Show single vertex strong component subgraph of G subset Suppose Theorem tournament underlying graph vertices adjacent vertices of G weighted graph