C4-Saturation Obstruction for Comb-Cores: A Certificate-Based Approach to Edge-Completion
Year: 2026
Type: article
Abstract: We prove that a specific comb-core graph H on 7 vertices, while avoiding all power-of-twocycle lengths, becomes C4-saturated relative to its degree-deficit vertices. This saturationproperty implies that every edge-completion of H achieving minimum degree δ ≥ 3 mustcontain a 4-cycle. We provide explicit 3-path witnesses as checkable certificates for thesaturation claim.
Author: Gebendorfer, Jonas Jakob
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7126258282
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