相关论文: ASP-Completeness of Hamiltonicity in Grid Graphs, …

We present a matching and LP based heuristic algorithm that decides graph non-Hamiltonicity. Each of the $n!$ Hamilton cycles in a complete directed graph on $n+1$ vertices corresponds with each of the $n!$ $n$-permutation matrices $P$,…

Pencil puzzles are puzzles that can be solved by writing down solutions on a paper, using only logical reasoning. In this paper, we utilize the "T-metacell" framework developed by Tang and the MIT Hardness Group to prove the NP-completeness…

The Hamiltonian cycle problem is to decide whether a given graph has a Hamiltonian cycle. Bertossi and Bonuccelli (1986, Information Processing Letters, 23, 195-200) proved that the Hamiltonian Cycle Problem is NP-Complete even for…

We prove that every locally Hamiltonian graph with $n\ge 3$ vertices and possibly with multiple edges has at least $3n-6$ edges with equality if and only if it triangulates the sphere. As a consequence, every edge-maximal embedding of a…

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two…

It is a longstanding conjecture that every simple drawing of a complete graph on $n \geq 3$ vertices contains a crossing-free Hamiltonian cycle. We strengthen this conjecture to "there exists a crossing-free Hamiltonian path between each…

All or Nothing, Water Walk, and Remembered Length are pencil puzzles that involve constructing a continuous loop on a rectangular grid under specific constraints. In this paper, we analyze their computational complexity using the T-metacell…

A supergrid graph is a finite vertex-induced subgraph of the infinite graph whose vertex set consists of all points of the plane with integer coordinates and in which two vertices are adjacent if the difference of their x or y coordinates…

A graph is Hamiltonian if it contains a cycle which goes through all vertices exactly once. Determining if a graph is Hamiltonian is known as a NP-complete problem and no satisfactory characterization for these graphs has been found. In…

Motivated by a relaxed notion of the celebrated Hamiltonian cycle, this paper investigates its variant, parity Hamiltonian cycle (PHC): A PHC of a graph is a closed walk which visits every vertex an odd number of times, where we remark that…

We show that every triangulation (maximal planar graph) on $n\ge 6$ vertices can be flipped into a Hamiltonian triangulation using a sequence of less than $n/2$ combinatorial edge flips. The previously best upper bound uses $4$-connectivity…

Barnette's conjecture is an unsolved problem in graph theory. The problem states that every 3-regular (cubic), 3-connected, planar, bipartite (Barnette) graph is Hamiltonian. Partial results have been derived with restrictions on number of…

A Hamiltonian path (cycle) in a graph is a path (cycle, respectively) which passes through all of its vertices. The problems of deciding the existence of a Hamiltonian cycle (path) in an input graph are well known to be NP-complete, and…

We exactly settle the complexity of graph realization, graph rigidity, and graph global rigidity as applied to three types of graphs: "globally noncrossing" graphs, which avoid crossings in all of their configurations; matchstick graphs,…

The semi-random graph process is an adaptive random graph process in which an online algorithm is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the algorithm independently and uniformly at…

In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…

A circle of an infinite locally finite graph $G$ is the imagine of a homeomorphic mapping of the unit circle $S^1$ in $|G|$, the Freudenthal compactification of $G$. A circle of $G$ is Hamiltonian if it meets every vertex (and then every…

An st-path is a path with the end-vertices s and t. An s-path is a path with an end-vertex s. The results of this paper include necessary and sufficient conditions for a {claw, net}-free graph G with given two different vertices s, t and an…

Although, the Hamiltonicity of solid grid graphs are polynomial-time decidable, the complexity of the longest cycle problem in these graphs is still open. In this paper, by presenting a linear-time constant-factor approximation algorithm,…

The generalised Sudoku problem with $N$ symbols is known to be NP-complete, and hence is equivalent to any other NP-complete problem, even for the standard restricted version where $N$ is a perfect square. In particular, generalised Sudoku…