arXiv subjects
Publications and source records attributed to Yeonsu Chang.
We show that there is a fixed planar graph $H$, namely the $5 \times 5$ grid, such that Max Independent Set remains NP-hard in $H$-induced-minor-free graphs. This refutes the Dallard--Milani\v{c}--\v{S}torgel conjecture and a weakening of it by Gartland and Lokshtanov, and by Korhonen.
Reduced parameters [BKW, JCTB '26; BKRT, SODA '22] are defined via contraction sequences. Based on this framework, we introduce the reduced component max-leaf, denoted by $\operatorname{cml}^\downarrow$, where component max-leaf is the maximum number of leaves in any spanning tree of any connected component. Reduced component max-leaf is strictly sandwiched between clique-width and reduced bandwidth, it is bounded in unit interval graphs, and unbounded in planar graphs. We design polynomial-time algorithms for problems such as \textsc{Maximum Induced $d$-Regular Subgraph} and \textsc{Induced Disjoint Paths} in graphs given with a contraction sequence witnessing low $\operatorname{cml}^\downarrow$, unifying and extending tractability results for classes of bounded clique-width and unit interval graphs. We get the following collapses in sparse classes of bounded $\operatorname{cml}^\downarrow$: bounded maximum degree implies bounded treewidth, whereas $K_{t,t}$-subgraph-freeness implies strongly sublinear treewidth; we show the latter, more generally, for classes of bounded reduced cutwidth. We establish the former result by showing that graphs with bounded $\operatorname{cml}^\downarrow$ admit balanced separators dominated by a bounded number of vertices. We then showcase an application of the reduced parameters to establishing non-transducibility results. We prove that for most reduced parameters $p^\downarrow$ (including reduced bandwidth), the family of classes of bounded $p^\downarrow$ is closed under first-order transductions. We then answer a question of [BKW '26] by showing that the 3-dimensional grids have unbounded reduced bandwidth. As the class of planar graphs (or any class of bounded genus) has bounded reduced bandwidth [BKW '26], this reproves a recent result [GPP, LICS '25] that planar graphs do not first-order transduce the 3-dimensional grids.
The class of even-hole-free graphs has been extensively studied on its own and on its relation to perfect graphs. In this paper, we study the $\chi$-boundedness of even-hole-free graphs which itself is an important topic in graph theory. In particular, we prove that every even-hole-free graph $G$ without induced 7-vertex paths satisfies $\chi(G)\le \lceil\frac{5}{4}\omega(G)\rceil$, where $\chi(G)$ and $\omega(G)$ denote the chromatic number and clique number of $G$, respectively. This bound is optimal. Our result strictly extends the result of Karthick and Maffary \cite{KM19} on even-hole-free graphs without induced 6-vertex paths, and implies that even-hole-free graphs without induced 7-vertex paths satisfy Reed's Conjecture. Our proof relies on a heavy structural analysis on a maximal substructure called a nice blowup of a five-cycle and can be viewed for graphs in which all holes are of length five (graphs with all holes having the same length gain increasing interest in recent years \cite{COOK202496}). Our result gives a partial answer to a conjecture of Wang and Wu \cite{WW25} on graphs in which all holes are of length 5. One of the key technical ingredients is a technical lemma proved via clique cutset argument combined with the idea of Infinite Descent Method (often used in number theory).
Horiyama et al. (AAAI 2024) considered the problem of generating instances with a unique minimum vertex cover under certain conditions. The Minimum Pre-assignment for Uniquification of Minimum Vertex Cover problem (shortly Min PAU-VC) is the problem, for given a graph $G$, to find a minimum set $S$ of vertices in $G$ such that among all minimum vertex covers of $G$, exactly one contains $S$. We show that Min PAU-VC is fixed-parameter tractable parameterized by clique-width, which improves an exponential algorithm for trees given by Horiyama et al. Among natural graph classes with unbounded clique-width, we show that the problem can be solved in linear time on split graphs and unit interval graphs.
The $r$-flip-width of a graph, for $r\in \mathbb{N}\cup \{\infty\}$, is a graph parameter defined in terms of a variant of the cops and robber game, called the flipper game, and it was introduced by Toru\'{n}czyk (FOCS 2023). We prove that for every $r\in (\mathbb{N}\setminus \{1\})\cup \{\infty\}$, the class of graphs of $r$-flip-width at most $2$ is exactly the class of ($C_5$, bull, gem, co-gem)-free graphs, which are known as totally decomposable graphs with respect to bi-joins.
We introduce graph width parameters, called $\alpha$-edge-crossing width and edge-crossing width. These are defined in terms of the number of edges crossing a bag of a tree-cut decomposition. They are motivated by edge-cut width, recently introduced by Brand et al. (WG 2022). We show that edge-crossing width is equivalent to the known parameter tree-partition-width. On the other hand, $\alpha$-edge-crossing width is a new parameter; tree-cut width and $\alpha$-edge-crossing width are incomparable, and they both lie between tree-partition-width and edge-cut width. We provide an algorithm that, for a given $n$-vertex graph $G$ and integers $k$ and $\alpha$, in time $2^{O((\alpha+k)\log (\alpha+k))}n^2$ either outputs a tree-cut decomposition certifying that the $\alpha$-edge-crossing width of $G$ is at most $2\alpha^2+5k$ or confirms that the $\alpha$-edge-crossing width of $G$ is more than $k$. As applications, for every fixed $\alpha$, we obtain FPT algorithms for the List Coloring and Precoloring Extension problems parameterized by $\alpha$-edge-crossing width. They were known to be W[1]-hard parameterized by tree-partition-width, and FPT parameterized by edge-cut width, and we close the complexity gap between these two parameters.