arXiv subjects

Hiraku Morimoto

Publications and source records attributed to Hiraku Morimoto.

2 recordsLinked to original sources

arXiv2026

On the Complexity of Forcing and Anti-Forcing Minimum Cuts

For an instance of a combinatorial optimization problem, a \emph{forcing set} is a set of elements such that there is a unique optimal solution including it. Symmetrically, an \emph{anti-forcing set} is a set of elements such that there is a unique optimal solution excluding it. In this paper, we study the problems of computing smallest forcing and anti-forcing sets for two classical cut problems, \textsc{Global Min Cut} and \textsc{Min $s$--$t$ Cut}. We also consider variants in which the optimal cut to be uniquely determined is given as input. For each of these problems, we either give a polynomial-time algorithm or prove \NP-completeness.

cs.DS↗

arXiv2026

Treewidth of the $n \times n$ toroidal grid

In this paper, we show that the treewidth of the $n \times n$ toroidal grid is $2n-1$ for all $n \ge 5$. This closes the gap between the previously known upper bound of $2n-1$ (Ellis and Warren, DAM 2008) and the lower bound of $2n-2$ (Kiyomi, Okamoto, and Otachi, DAM 2016). To establish the matching lower bound, we construct a bramble of maximum order by utilizing maximum components obtained after removing $2n-1$ vertices. Our construction relies on the vertex-isoperimetric properties of the infinite grid to establish tight lower bounds on neighborhood sizes, combined with a careful analysis of balls of radius $n/2-1$ and their boundaries to overcome structural obstructions when $n$ is even.

math.CO↗