arXiv subjects

Tatsuhiro Suga

Publications and source records attributed to Tatsuhiro Suga.

5 recordsLinked to original sources

arXiv2026

Parameterized Complexity of Odd Domination and its Generalization

In the \textsc{Odd Domination} problem, given a graph $G$ and a positive integer $k$, the task is to determine whether there exists a vertex subset $D$ of $G$ such that the closed neighborhood of each vertex in $G$ contains an odd number of vertices from $D$. In this paper, we investigate the computational complexity of the problem. When parameterized by the solution size $k$, we establish W[1]-hardness on some restricted graphs and a sharp boundary between fixed-parameter tractability and W[1]-hardness with respect to the girth of the input graph. Then, we address the problem when parameterized by several structural graph parameters. Furthermore, we investigate the parameterized complexity of \textsc{Parity Domination}, which is a generalization of \textsc{Odd Domination}.

cs.DS↗

arXiv2025

Solution Discovery for Vertex Cover, Independent Set, Dominating Set, and Feedback Vertex Set

In the solution discovery problem for a search problem on graphs, we are given an initial placement of $k$ tokens on the vertices of a graph and asked whether this placement can be transformed into a feasible solution by applying a small number of modifications. In this paper, we study the computational complexity of solution discovery for several fundamental vertex-subset problems on graphs, namely Vertex Cover Discovery, Independent Set Discovery, Dominating Set Discovery, and Feedback Vertex Set Discovery. We first present XP algorithms for all four problems parameterized by clique-width. We then prove that Vertex Cover Discovery, Independent Set Discovery, and Feedback Vertex Set Discovery are NP-complete for chordal graphs and graphs of diameter 2, which have unbounded clique-width. In contrast to these hardness results, we show that all three problems can be solved in polynomial time on split graphs. Furthermore, we design an FPT algorithm for Feedback Vertex Set Discovery parameterized by the number of tokens.

cs.DS↗

arXiv2025

Coloring Reconfiguration under Color Swapping

In the \textsc{Coloring Reconfiguration} problem, we are given two proper $k$-colorings of a graph and asked to decide whether one can be transformed into the other by repeatedly applying a specified recoloring rule, while maintaining a proper coloring throughout. For this problem, two recoloring rules have been widely studied: \emph{single-vertex recoloring} and \emph{Kempe chain recoloring}. In this paper, we introduce a new rule, called \emph{color swapping}, where two adjacent vertices may exchange their colors, so that the resulting coloring remains proper, and study the computational complexity of the problem under this rule. We first establish a complexity dichotomy with respect to $k$: the problem is solvable in polynomial time for $k \leq 2$, and is PSPACE-complete for $k \geq 3$. We further show that the problem remains PSPACE-complete even on restricted graph classes, including bipartite graphs, split graphs, and planar graphs of bounded degree. In contrast, we present polynomial-time algorithms for several graph classes: for paths when $k = 3$, for split graphs when $k$ is fixed, and for cographs when $k$ is arbitrary.

cs.DS↗

arXiv2025

Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules

In reconfiguration problems, we are given two feasible solutions to a graph problem and asked whether one can be transformed into the other via a sequence of feasible intermediate solutions under a given reconfiguration rule. While earlier work focused on modifying a single element at a time, recent studies have started examining how different rules impact computational complexity. Motivated by recent progress, we study Independent Set Reconfiguration (ISR) and Vertex Cover Reconfiguration (VCR) under the $k$-Token Jumping ($k$-TJ) and $k$-Token Sliding ($k$-TS) models. In $k$-TJ, up to $k$ vertices may be replaced, while $k$-TS additionally requires a perfect matching between removed and added vertices. It is known that the complexity of ISR crucially depends on $k$, ranging from PSPACE-complete and NP-complete to polynomial-time solvable. In this paper, we further explore the gradient of computational complexity of the problems. We first show that ISR under $k$-TJ with $k = |I| - \mu$ remains NP-hard when $\mu$ is any fixed positive integer and the input graph is restricted to graphs of maximum degree 3 or planar graphs of maximum degree 4, where $|I|$ is the size of feasible solutions. In addition, we prove that the problem belongs to NP not only for $\mu=O(1)$ but also for $\mu = O(\log |I|)$. In contrast, we show that VCR under $k$-TJ is in XP when parameterized by $\mu = |S| - k$, where $|S|$ is the size of feasible solutions. Furthermore, we establish the PSPACE-completeness of ISR and VCR under both $k$-TJ and $k$-TS on several graph classes, for fixed $k$ as well as superconstant $k$ relative to the size of feasible solutions.

cs.CC↗

arXiv2025

Changing Induced Subgraph Isomorphisms Under Extended Reconfiguration Rules

In a reconfiguration problem, we are given two feasible solutions of a combinatorial problem and our goal is to determine whether it is possible to reconfigure one into the other, with the steps dictated by specific reconfiguration rules. Traditionally, most studies on reconfiguration problems have focused on rules that allow changing a single element at a time. In contrast, this paper considers scenarios in which $k \ge 2$ elements can be changed simultaneously. We investigate the general reconfiguration problem of isomorphisms. For the Induced Subgraph Isomorphism Reconfiguration problem, we show that the problem remains $\textsf{PSPACE}$-complete even under stringent constraints on the pattern graph when $k$ is constant. We then give two meta-theorems applicable when $k$ is slightly less than the number of vertices in the pattern graph. In addition, we investigate the complexity of the Independent Set Reconfiguration problem, which is a special case of the Induced Subgraph Isomorphism Reconfiguration problem.

cs.DS↗