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A note on minimum graphs with girth pair (4, 2 l + 1)
Author(s) -
Hanson Denis,
Wang Ping,
Macgillivray Gary
Publication year - 1994
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.3190180403
Subject(s) - combinatorics , mathematics , girth (graph theory) , conjecture , graph , constant (computer programming) , discrete mathematics , odd graph , chordal graph , 1 planar graph , computer science , programming language
We show that the size of a smallest connected k ‐regular graph with girth pair (4, 2 l + 1) is within a constant of (2 l + 1) k /2. In so doing we disprove a conjecture of Harary and Kovacs.