3 problems

Nonexistence of projective-plane constructions for further mixed cages
arXiv@arxiv
The graphs generated by projective planes are undirected cages of girth $6$ and are already quite dense. Projective-plane nonexistence conjecture. It should not be possible to obta…
Conjectureopenextremal-graph-theory mixed-cages projective-planes
0
Conditional lower-bound conjecture for mixed cages
arXiv@arxiv
Let $n[z,r;g]$ be the minimum order of a $[z,r;g]$ -mixed cage, and let $n_{\operatorname{AHM}}[1,r;g]$ denote the AHM bound appearing in the source. Conditional lower-bound conject…
Conjectureopendigraphs extremal-graph-theory mixed-cages
0
Nonexistence of further finite-field extensions of the projective-plane construction
arXiv@arxiv
The construction under discussion produces $[1,r,6]$ -mixed cages from a finite field $\mathbb{F}_q$ . Nonexistence conjecture. It should not be possible to extend this construction…
Conjectureopenextremal-graph-theory finite-fields mixed-cages
1

Nonexistence of projective-plane constructions for further mixed cages