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Class 1 conditions depending on the minimum degree and the number of vertices of maximum degree
Author(s) -
Niessen Thomas,
Volkmann Lutz
Publication year - 1990
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.3190140211
Subject(s) - mathematics , degree (music) , combinatorics , edge coloring , discrete mathematics , class (philosophy) , brooks' theorem , simple graph , graph , simple (philosophy) , frequency partition of a graph , 1 planar graph , chordal graph , graph power , line graph , computer science , philosophy , physics , epistemology , artificial intelligence , acoustics
Abstract A graph is called Class 1 if the chromatic index equals the maximum degree. We prove sufficient conditions for simple graphs to be Class 1. Using these conditions we improve results on some edge‐coloring theorems of Chetwynd and Hilton. We also improve a theorem concerning the 1‐factorization of regular graphs of high degree.