Bartlomiej Bychawski

collaborators

4 papers

math.CO2026

Asymptotical results on the automorphism groups of canonical double cover of graphs

Bartłomiej Bychawski, Ademir Hujdurović, Đorđe Mitrović +1

The canonical double cover $B X$ of a graph $X$ is the direct product $X \times K_{2}$ . A graph $X$ is stable if every automorphism of $B X$ is induced by automorphisms of $X$ and $K_{2}$ …

math.AC2026

Sums of squares on curves and surfaces

Bartłomiej Bychawski, Bartosz Głowacki, Tomasz Kowalczyk

We study sums of higher even powers in the coordinate rings of singular planar curves $x^{M} = y^{m}$ for coprime positive integers $m < M$ . We then show that the $2 s$ -Pythagoras number of…

math.CO2024

Classification of unstable circulants of square-free order

Bartłomiej Bychawski

In this paper we prove that for circulants of squarefree orders Wilson's conjecture hold, that is each nontrivially unstable circulant of such order has Wilson type. We show that a…

math.CO2024

Constructions of graphs with any possible two-fold automorphism and automorphism groups

Bartłomiej Bychawski

It is known that the canonical double cover of any connected nonbipartite graph have an automorphism group of the form $H ⋊ Z_{2}$ , where $H$ is the set of automorphis…