Related papers: Col is PSPACE-complete on Triangular Grids
We prove computational intractability of variants of checkers: (1) deciding whether there is a move that forces the other player to win in one move is NP-complete; (2) checkers where players must always be able to jump on their turn is…
We study the algorithmic complexity of Maker-Breaker games played on the edge sets of general graphs. We mainly consider the perfect matching game and the $H$-game. Maker wins if she claims the edges of a perfect matching in the first, and…
This paper introduces a new reconfiguration problem of matchings in a triangular grid graph. In this problem, we are given a nearly perfect matching in which each matching edge is labeled, and aim to transform it to a target matching by…
We study the computational complexity of distance games, a class of combinatorial games played on graphs. A move consists of colouring an uncoloured vertex subject to it not being at certain distances determined by two sets, D and S. D is…
We use Menger's Theorem and K\"onig's Line Colouring Theorem to show that in any tripartite graph with two complete (bipartite) sides the maximum number of pairwise edge-disjoint triangles equals the minimum number of edges that meet all…
We investigate the space complexity of certain perfect matching problems over bipartite graphs embedded on surfaces of constant genus (orientable or non-orientable). We show that the problems of deciding whether such graphs have (1) a…
We demonstrate that when a graph exhibits a specific type of symmetry, it satisfies the Union Closed Conjecture(UCC). Additionally, we show that certain graph classes, such as Cylindrical Grid Graphs and Torus Grid Graphs also satisfy the…
We analyze the computational complexity of the video game "CELESTE" and prove that solving a generalized level in it is NP-Complete. Further, we also show how, upon introducing a small change in the game mechanics (adding a new game…
In the online graph coloring problem, vertices from a graph G, known in advance, arrive in an online fashion and an algorithm must immediately assign a color to each incoming vertex v so that the revealed graph is properly colored. The…
The 3-coloring of hereditary graph classes has been a deeply-researched problem in the last decade. A hereditary graph class is characterized by a (possibly infinite) list of minimal forbidden induced subgraphs $H_1,H_2,\ldots$; the graphs…
We consider the problem of covering a graph with a given number of induced subgraphs so that the maximum number of vertices in each subgraph is minimized. We prove NP-completeness of the problem, prove lower bounds, and give approximation…
We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of…
We show that c-planarity is solvable in quadratic time for flat clustered graphs with three clusters if the combinatorial embedding of the underlying graph is fixed. In simpler graph-theoretical terms our result can be viewed as follows.…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
We investigate the parameterized complexity of several problems formalizing cluster identification in graphs. In other words we ask whether a graph contains a large enough and sufficiently connected subgraph. We study here three relaxations…
In this study we consider the problem of triangulated graphs. Precisely we give a necessary and sufficient condition for a graph to be triangulated. This give an alternative characterization of triangulated graphs. Our method is based on…
The game domination number is a graph invariant that arises from a game, which is related to graph domination in a similar way as the game chromatic number is related to graph coloring. In this paper we show that verifying whether the game…
Finding Hamitonian Cycles in square grid graphs is a well studied and important questions. More recent work has extended these results to triangular and hexagonal grids, as well as further restricted versions. In this paper, we examine a…
We conjecture that the balanced complete bipartite graph $K_{\lfloor n/2 \rfloor,\lceil n/2 \rceil}$ contains more cycles than any other $n$-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent…
In this paper, we resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance:…