Prosenjit Bose

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20242026

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math.CO2026

Cops and robber in graphs with bounded vertex cover number

Prosenjit Bose, Louis Esperet, JÄdrzej Hodor +3

Meyniel's conjecture states that $n$ -vertex connected graphs have cop number $O (n)$ . The current best known upper bound is $n / 2^{(1 - o (1)) l o g n}$ , proved independentl…

math.CO2024

The basis number of 1-planar graphs

Saman Bazargani, Therese Biedl, Prosenjit Bose +2

Let $B$ be a set of Eulerian subgraphs of a graph $G$ . We say $B$ forms a $k$ -basis if it is a minimum set that generates the cycle space of $G$ , and any edge of $G$ lies in at mos…

math.CO2024

On the $d$ -independence number in 1-planar graphs

Therese Biedl, Prosenjit Bose, Babak Miraftab

The $d$ -independence number of a graph $G$ is the largest possible size of an independent set $I$ in $G$ where each vertex of $I$ has degree at least $d$ in $G$ . Upper bounds for t…

Cops and robber in graphs with bounded vertex cover number

The basis number of 1-planar graphs

On the d-independence number in 1-planar graphs

On the $d$ -independence number in 1-planar graphs