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The chromatic index of graphs of even order with many edges
Author(s) -
Chetwynd A. G.,
Hilton A. J. W.
Publication year - 1984
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.3190080403
Subject(s) - combinatorics , mathematics , conjecture , vertex (graph theory) , graph , degree (music) , chromatic scale , edge coloring , order (exchange) , class (philosophy) , discrete mathematics , graph power , line graph , computer science , physics , finance , acoustics , economics , artificial intelligence
We show that, for r = 1, 2, a graph G with 2 n + 2 (≥6) vertices and maximum degree 2 n + 1 ‐ r is of Class 2 if and only if | E ( G / v )| > ( 2 2 n +1 ) ‐ rn , where v is a vertex of G of minimum degree, and we make a conjecture for 1 ≤ r ≤ n , of which this result is a special case. For r = 1 this result is due to Plantholt.