Sizes of the extremal girth 5 graphs of orders from 40 to 49
J\"orgen Backelin
TL;DR
This paper determines the maximum sizes of extremal graphs with girth 5 for orders 40 to 49, advancing knowledge of Turán type numbers and filling gaps in OEIS sequence A006856.
Contribution
It provides exact Turán type numbers for graphs with girth 5 for orders 40 to 49, and offers estimates for the remaining cases, expanding the known sequence.
Findings
Exact sizes for graphs with girth 5 for orders 40-49
Complete determination of 43 out of 50 OEIS sequence entries
Estimates provided for the remaining 7 cases
Abstract
The Tur\'an type numbers for graphs without 3-cycles and 4-cycles are determined for vertex numbers from 40 to 49 inclusive. Hence, now, 43 of the first 50 numbers of OEIS A006856 are known. Estimates for the remaining seven numbers are presented.
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Taxonomy
TopicsGraph theory and applications · Limits and Structures in Graph Theory · Graph Labeling and Dimension Problems