3 problems

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The independence-number case of the Bollobás–Nikiforov conjecture for $K_4$ -free graphs
Let $G$ be a $K_4$ -free graph on $n$ vertices with $m$ edges, let $\alpha(G)$ denote its independence number, and let … be its adjacency eigenvalues. Independence-number conjecture…
Conjectureopenextremal-graph-theory k4-free-graphs spectral-graph-theoryarXiv posted 2 days ago
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Győri–Keszegh's greedy-partition triangle conjecture for $K_4$ -free graphs
Győri–Keszegh's conjecture. For every such graph $G$ and every greedy partition $P$ ,
Conjectureopenextremal-graph-theory k4-free-graphs triangle-packingsarXiv posted 2 days ago
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Erdős's K4-free bipartization conjecture
Let $G$ be a $K_4$ -free graph on $n$ vertices, and let $\tau_{B}(G)$ denote the minimum number of edges whose deletion makes $G$ bipartite. Erdős's conjecture. It should be possibl…
Conjectureopenbipartite-graphs extremal-graph-theory k4-free-graphsarXiv posted 2 days ago

The independence-number case of the Bollobás–Nikiforov conjecture for K4K_4K4​-free graphs