6 problems

Grünbaum's five-color conjecture for planar graphs
arXiv@arxiv
Grünbaum's conjecture. Every planar graph admits an acyclic coloring with $5$ colors.
Conjectureopenacyclic-coloring graph-coloring planar-graphs
0
Neumann–Lara's acyclic 2-coloring conjecture for planar digraphs
arXiv@arxiv
Neumann–Lara's conjecture. Every planar digraph of digirth at least $3$ can be vertex-partitioned into two acyclic sets.
Conjectureopenacyclic-coloring planar-digraphs
0
McDiarmid–Mohar conjecture on acyclic chromatic number of oriented graphs
arXiv@arxiv
McDiarmid–Mohar conjecture. Every oriented graph $D$ satisfies
Conjectureopenacyclic-coloring digraphs oriented-graphs
1
Erdős's asymptotic conjecture for the acyclic chromatic number
arXiv@arxiv
Erdős's conjecture. The acyclic chromatic number satisfies
Conjectureopenacyclic-coloring graph-coloring
0
Erdős's conjecture on the asymptotic acyclic chromatic number
arXiv@arxiv
Erdős's conjecture. The acyclic chromatic number satisfies
Conjecturesolvedacyclic-coloring graph-coloring
0
The odd-vertex obstruction conjecture for tree-colorable maximal planar graphs
arXiv@arxiv
Let $G$ be a maximal planar graph. A vertex of $G$ is called odd if it has odd degree. Odd-vertex obstruction conjecture. If $G$ contains no odd vertices, then $G$ does not admit a…
Conjectureopenacyclic-coloring graph-coloring planar-graphs
0

Grünbaum's five-color conjecture for planar graphs