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Short proofs of classical theorems
Author(s) -
Bondy J. A.
Publication year - 2003
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.10135
Subject(s) - mathematical proof , mathematics , brooks' theorem , combinatorics , vertex (graph theory) , discrete mathematics , proofs of fermat's little theorem , graph , fundamental theorem , compactness theorem , fixed point theorem , 1 planar graph , line graph , geometry
We give proofs of Ore's theorem on Hamilton circuits, Brooks' theorem on vertex coloring, and Vizing's theorem on edge coloring, as well as the Chvátal‐Lovász theorem on semi‐kernels, a theorem of Lu on spanning arborescences of tournaments, and a theorem of Gutin on diameters of orientations of graphs. These proofs, while not radically different from existing ones, are perhaps simpler and more natural. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 159–165, 2003
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