Pith. sign in

REVIEW 3 cited by

Zero Forcing and Vertex Independence Number on Cubic and Subcubic Graphs

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 2410.21724 v2 pith:SLRTUIFA submitted 2024-10-29 math.CO

Houston Schuerger , Nathan Warnberg , Michael Young This is my paper · ORCID
classification math.CO
keywords graphscubicalphanumbersubcubicforcingindependencetxgraffiti
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

Motivated by a conjecture from the automated conjecturing program TxGraffiti, in this paper the relationship between the zero forcing number, $Z(G)$, and the vertex independence number, $\alpha(G)$, of cubic and subcubic graphs is explored. TxGraffiti conjectures that for all connected cubic graphs $G$, that are not $K_4$, $Z(G) \leq \alpha(G) + 1$. This work uses decycling partitions of upper-embeddable graphs to show that almost all cubic graphs satisfy $Z(G) \leq \alpha(G) + 2$, provides an infinite family of cubic graphs where $Z(G) = \alpha(G) + 1$, and extends known bounds to subcubic graphs.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

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

  1. A counterexample to the zero forcing versus independence conjecture for cubic and subcubic graphs

    math.CO 2026-07 accept novelty 7.0 of 10

    Explicit connected subcubic and cubic graphs attain Z = α + 2, refuting the TxGraffiti conjecture that Z ≤ α + 1 for connected graphs with Δ ≤ 3.

  2. In Reverie Together: Ten Years of Mathematical Discovery with a Machine Collaborator

    cs.DM 2025-07 conditional novelty 7.0 of 10 partial

    Four machine-generated open conjectures relating independence, zero forcing, domination, and matching invariants in graphs are presented, each with empirical support but no proof.

  3. Connected forcing density and related problems

    math.CO 2025-07 conditional novelty 6.0 of 10

    A graph is CF-dense when every vertex lies in some minimum connected forcing set; the paper characterizes CF-dense trees and counts connected forcing sets in trees.

Pith tools