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Sizes of the extremal girth 5 graphs of orders from 40 to 49

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arxiv 1511.08128 v1 pith:YLC25U6Q submitted 2015-11-25 math.CO

Jörgen Backelin This is my paper · ORCID
classification math.CO
keywords numberscyclesgraphsa006856determinedestimatesextremalfirst
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Counterexamples, Spectral Obstructions, and Deletion Stability for WOW-284

    math.CO 2026-07 accept novelty 6.5 of 10 partial

    WOW-284 fails on explicit graphs of orders 38,39,40,42,50; regular strict counterexamples need degree ≥6 and diameter ≤4, with exact LP order bounds and Hoffman–Singleton deletion radius five.

  2. Improved lower bounds on the maximum size of graphs with girth 5

    math.CO 2025-08 accept novelty 6.0 of 10

    A new hill-climbing algorithm improves the best known lower bounds on ex(n;{C3,C4}) for all n in {74,...,198} except n = 96,97.

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