4 problems

3-colorability conjecture for string graphs of sufficiently large odd girth
arXiv@arxiv
Let $k$ be an integer, and consider the class of string graphs whose odd girth is at least $k$ . String-graph coloring conjecture. There is an integer $k$ such that the class of str…
Conjectureopengraph-coloring odd-girth string-graphs
0
Maximum spectral radius conjecture for odd-cycle-free non-bipartite graphs
arXiv@arxiv
Maximum spectral radius conjecture. If $G$ contains no member of $\{C_3,C_5,\ldots,C_{2k+1}\}$ and is non-bipartite, then
Conjectureopenextremal-graph-theory odd-girth spectral-graph-theory
0
Odd-girth multicoloring conjecture for hexagonal graphs
arXiv@arxiv
Odd-girth multicoloring conjecture. If $G$ has odd-girth at least $2k+1$ , then $G$ is $(2k+1,k)$ -colorable.
Conjectureopengraph-coloring multicoloring odd-girth
0
Manane's bounded odd-girth homomorphism conjecture
arXiv@arxiv
Let $k$ be a positive integer and let $\mathcal{C}$ be a class of graphs. Say that $\mathcal{C}$ is bounded by a graph $H$ if every graph in $\mathcal{C}$ admits a homomorphism to…
Conjecturesolvedgraph-homomorphisms graph-powers odd-girth
0

3-colorability conjecture for string graphs of sufficiently large odd girth