Pith. sign in

REVIEW 1 cited by

Forbidding induced even cycles in a graph: typical structure and counting

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1507.04944 v1 pith:DKTTET2P submitted 2015-07-17 math.CO

Jaehoon Kim , Daniela Kühn , Deryk Osthus , Timothy Townsend This is my paper · ORCID
classification math.CO
keywords inducedstructuretypicalcyclegraphswithoutapproachapproximate
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We determine, for all $k\geq 6$, the typical structure of graphs that do not contain an induced $2k$-cycle. This verifies a conjecture of Balogh and Butterfield. Surprisingly, the typical structure of such graphs is richer than that encountered in related results. The approach we take also yields an approximate result on the typical structure of graphs without an induced $8$-cycle or without an induced $10$-cycle.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. The asymptotic $\chi$-boundedness of hereditary families

    math.CO 2025-06 conditional novelty 7.0 of 10

    For every tree T, almost all T-free graphs satisfy chi=omega, and for every cycle C_k except C_6, almost all C_k-free graphs satisfy chi=omega; C_6-free graphs are asymptotically chi-bounded with f(w)=(1+o(1))w^2/log w.

Pith tools