N. Karol

activity

20222026

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math.CO2022

Restriction on minimum degree in the contractible sets problem

Nikolai Karol

Let $G$ be a $3$ -connected graph. A set $W \subset V (G)$ is called contractible if $G (W)$ is a connected graph and $G - W$ is a $2$ -connected graph. In 1994, McCuaig and Ota conjec…

math.CO2022

An existence criterion for a cycle such that the vertex set beyond this cycle is independent

Nikolai Karol

We prove that if $G$ is a 2-connected graph with $δ (G) ⩾ \frac{v ( G ) + 2}{3}$ then $G$ has a cycle $W$ such that $V (G - W)$ is independent. This result is best possible in t…