2 problems

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Clique-intersection conjecture for non-Hamiltonicity in $C_8$
Let $G\in C_8$ be a graph in the eighth subclass of the paper's partition of random Apollonian networks, and let $Q_1,Q_2,Q_3$ denote the maximal cliques relevant to the discussed…
Conjectureopenclique-trees hamiltonian-graphs random-apollonian-networksarXiv posted 2 days ago
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Toughness conjecture for the class $C_8$ of random Apollonian networks
Let $C_8$ be the eighth subclass in the partition of random Apollonian networks used in the paper, and let $\tau(G)$ denote graph toughness. The $C_8$ toughness conjecture. Every g…
Conjectureopengraph-theory random-apollonian-networks toughnessarXiv posted 2 days ago

Clique-intersection conjecture for non-Hamiltonicity in C8C_8C8​