More Constructions for Tur\'an's (3, 4)-Conjecture

TL;DR

This paper constructs numerous non-isomorphic complexes that satisfy Turán's (3, 4)-conjecture for specific vertex counts, expanding the known examples and supporting the conjecture's validity.

Contribution

It introduces new constructions of non-isomorphic complexes that attain Turán's (3, 4)-conjecture for n=3k+1 and n=3k+2 vertices.

Findings

Constructed 6^{k-1} complexes for n=3k+2 vertices.

Constructed 0.5*6^{k-1} complexes for n=3k+1 vertices.

Provided evidence supporting Turán's (3, 4)-conjecture.

Abstract

For Tur\'an's (3, 4)-conjecture, in the case of n = 3k+1 vertices, (.5)6^{k-1} non-isomorphic complexes are constructed that attain the conjecture. In the case of n = 3k+2 vertices, 6^{k-1} non-isomorphic complexes are constructed that attain the conjecture.