4 problems

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Rosenfeld's conjecture on oriented Hamilton paths in tournaments
A tournament is an oriented complete graph. An oriented Hamilton path is an oriented path containing every vertex of the tournament exactly once. Rosenfeld's conjecture. Every tour…
Conjecturesolvedhamilton-paths oriented-graphs tournamentsarXiv posted 2 days ago
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Ustimenko's eigenvalue conjecture for Lazebnik–Ustimenko–Woldar graphs
Ustimenko's conjecture. For all $(k,q)$ , every nontrivial eigenvalue of $D(k,q)$ , and therefore of $CD(k,q)$ , is at most $2\sqrt q$ .
Conjectureopenextremal-graph-theory hamilton-paths spectral-graph-theoryarXiv posted 2 days ago
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Kovács–Soltész conjecture on odd-cycle-creating Hamilton paths
Kovács–Soltész conjecture. The equality
Conjectureopencycles extremal-graph-theory hamilton-pathsarXiv posted 2 days ago
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Harcos–Soltész conjecture on $K_{2,4}$ -creating Hamilton paths
Harcos–Soltész conjecture. There is a constant $C>0$ such that
Conjectureopenextremal-graph-theory hamilton-paths permutationsarXiv posted 2 days ago

Rosenfeld's conjecture on oriented Hamilton paths in tournaments