3 problems

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Quasi-line graph 5/6 conjecture
A quasi-line graph is a graph in which the neighborhood of every vertex is covered by two cliques. For a graph $Q$ , let $\chi(Q)$ , $\omega(Q)$ , and $\Delta(Q)$ denote its chromatic…
Conjectureopengraph-coloring quasi-line-graphsarXiv posted 2 days ago
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Ben Rebea's conjecture on clique-family inequalities for quasi-line graphs
Ben Rebea's conjecture. The clique-family inequalities, together with the non-negativity constraints and clique inequalities, describe the stable set polytope of every quasi-line g…
Conjecturesolvedpolyhedral-combinatorics quasi-line-graphs stable-set-polytopesarXiv posted 2 days ago
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Superlocal Reed's conjecture
Superlocal Reed's conjecture. Every graph $G$ satisfies
Conjectureopengraph-colouring quasi-line-graphsarXiv posted 2 days ago

Quasi-line graph 5/6 conjecture