Explains how to reason and model combinatorially. Enables students to develop proficiency in fundamental discrete math problem solving in the manner that a calculus textbook develops competence in basic analysis problem solving. Stresses the systematic analysis of different possibilities, exploration of the logical structure of a problem and ingenuity. This edition contains many new exercises.
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ELEMENTS OF GRAPH THEORY
Representing Graphs Inside a Computer
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2-colorings a-z cut a-z flow adjacent algorithm arrangements balls binary sequences binomial binomial coefficients bipartite graph chosen coefficient combinatorial complete graph connected consecutive corners cube darkened squares depth-first search digits directed graph distinct objects distribute equation equivalence Euler cycle Example exponential generating function Ferrers diagram Find a recurrence formula four graph G graph in Figure graph theory Grundy number Hamilton circuit identical induction integer interval graph isomorphic kernel labeled least letters matching mathematical maximal flow minimal minimal spanning tree number of different number of edges number of vertices obtain outcomes pair partitions pattern inventory permutation pick pile planar graph player polynomial possible Prim's algorithm probability proof Prove recurrence relation regions rotation Section shortest path Show shown in Figure solve spanning tree subgraph subset Summary of Exercises Suppose symmetries Theorem total number tour undirected vertex vertices of degree winning