2 problems

0 votes0 replies0 views
Conjecture on fractional domatic number of planar graphs by girth
Planar girth fractional-domatic conjecture. For every integer $k\ge 1$ , if $3k-1\le g\le 3k+1$ , then
Conjectureopenfractional-domatic-number graph-girth planar-graphsarXiv posted 2 days ago
0 votes0 replies0 views
Gadouleau–Harms–Mertzios conjecture on fractional domatic number
Let $G$ be a connected graph, with minimum degree denoted by $4\delta(G)4$ and fractional domatic number by $4\operatorname{FDOM}(G)4$ . The known characterization states that…
Conjectureopenfractional-domatic-number graph-theoryarXiv posted 2 days ago

Conjecture on fractional domatic number of planar graphs by girth