Pith. sign in

REVIEW

Tur\'{a}n problem for mathcal{K}₄^--free signed graphs

Not yet reviewed by Pith; the record is open.

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 2306.06655 v1 pith:Q7MVKHUV submitted 2023-06-11 math.CO

Tur\'{a}n problem for mathcal{K}₄^--free signed graphs

classification math.CO
keywords mathcalsignedunbalancedfreegraphgraphsleqslantorder
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Suppose that $\dot{G}$ is an unbalanced signed graph of order $n$ with $e(\dot{G})$ edges. Let $\rho(\dot{G})$ be the spectral radius of $\dot{G}$, and $\mathcal{K}_4^-$ be the set of the unbalanced $K_4$. In this paper, we prove that if $\dot{G}$ is a $\mathcal{K}_4^-$-free unbalanced signed graph of order $n$, then $e(\dot{G})\leqslant \frac{n(n-1)}{2}-(n-3)$ and $\rho(\dot{G})\leqslant n-2$. Moreover, the extremal graphs are completely characterized.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.