2 problems

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The comparison conjecture for $A_\alpha$ -eigenvalue bounds
Let $G$ be a simple graph, with maximum degree $\Delta$ , minimum degree $\delta$ , and let $\alpha\in[0,1]$ . Comparison conjecture. One has … The inequality asserts that the lower b…
Conjectureopensimple-graphs spectral-graph-theoryarXiv posted 2 days ago
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The simple-graph degree-f arboricity conjecture
Simple-graph degree- $f$ arboricity conjecture. Truszczyński's degree- $f$ arboricity conjecture should hold for simple graphs: for every such $G$ and $f$ ,
Conjectureopenarboricity graph-coloring simple-graphsarXiv posted 2 days ago

The comparison conjecture for AαA_\alphaAα​-eigenvalue bounds