3 problems

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Dumitrescu–Heath–Schaefer asymptotic conjecture for thickness and sparse graphs
Dumitrescu–Heath–Schaefer conjecture. The minimum such constant is $c=1/16$ .
Conjecturerefutedextremal-graph-theory graph-thicknessarXiv posted 2 days ago
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Ganley–Heath conjecture on the book thickness of partial $k$ -trees
Let ${\mathcal{T}}_k$ be the class of graphs of treewidth at most $k$ , and let ${\textup{\textsf{bt}}_{}(G)}$ denote the book thickness of a graph $G$ . Ganley and Heath proved that…
Conjecturerefutedbook-embeddings graph-thickness treewidtharXiv posted 2 days ago
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Rubio-Montiel's conjecture on the 4-girth-thickness of the complete graph K_{10}
Rubio-Montiel's conjecture. The $4$ -girth-thickness of $K_{10}$ is $4$ . This conjecture is refuted in the paper, which shows that $\theta(4,K_{10})=3$ .
Conjectureopengraph-theory graph-thicknessarXiv posted 2 days ago

Dumitrescu–Heath–Schaefer asymptotic conjecture for thickness and sparse graphs