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Hamiltonian Cycles in Solid Grid Graphs (Extended Abstract)
"... ) Christopher Umans William Lenhart Computer Science Division Computer Science Department U.C. Berkeley Williams College umans@cs.berkeley.edu lenhart@cs.williams.edu Abstract A grid graph is a finite nodeinduced subgraph of the infinite twodimensional integer grid. A solid grid graph is a ..."
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grid graph without holes. For general grid graphs, the Hamiltonian cycle problem is known to be NPcomplete. We give a polynomialtime algorithm for the Hamiltonian cycle problem in solid grid graphs, resolving a longstanding open question posed in [IPS82]. In fact, our algorithm can identify
Hamiltonian Cycles in Triangular Grids
, 2006
"... We study the Hamiltonian Cycle problem in graphs induced by subsets of the vertices of the tiling of the plane with equilateral triangles. By analogy with grid graphs we call such graphs triangular grid graphs. Following the analogy, we define the class of solid triangular grid graphs. We prove that ..."
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We study the Hamiltonian Cycle problem in graphs induced by subsets of the vertices of the tiling of the plane with equilateral triangles. By analogy with grid graphs we call such graphs triangular grid graphs. Following the analogy, we define the class of solid triangular grid graphs. We prove
Hamiltonian properties of triangular grid graphs
 Discrete Mathematics, 308(24):6166 – 6188
, 2008
"... Abstract: It is known that all 2connected, linearly convex triangular grid graphs, with only one exception, are hamiltonian (Reay and Zamfirescu, 2000). In the paper, it is shown that this result holds for a wider class of connected, locally connected triangular grid graphs and, with more exception ..."
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exceptions, even for some general class of graphs. It is also shown that the HAMILTONIAN CYCLE problem is NPcomplete for triangular grid graphs. Copyright © 2006 IFAC
Spanning Closed Trail and Hamiltonian Cycle in Grid Graphs
, 1995
"... . In this paper we study a trail routing and a hamiltonian cycle in a class of grid graphs, polycube and polymino. A Spanning closed trail is an eulerian subgraph containing all vertices of a given graph. For general grid graphs we prove that the problem of finding that trail is NPcomplete and for ..."
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. In this paper we study a trail routing and a hamiltonian cycle in a class of grid graphs, polycube and polymino. A Spanning closed trail is an eulerian subgraph containing all vertices of a given graph. For general grid graphs we prove that the problem of finding that trail is NP
COMPLEXITY OF THE HAMILTONIAN CYCLE PROBLEM IN TRIANGULAR GRID GRAPHS
"... Abstract. A triangular grid graph is a finite induced subgraph of the infinite graph associated with the twodimensional triangular grid. We show that the problem Hamiltonian Cycle is NPcomplete for triangular grid graphs, while a hamiltonian cycle in connected, locally connected triangular grid gr ..."
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Abstract. A triangular grid graph is a finite induced subgraph of the infinite graph associated with the twodimensional triangular grid. We show that the problem Hamiltonian Cycle is NPcomplete for triangular grid graphs, while a hamiltonian cycle in connected, locally connected triangular grid
Hamiltonian Cycle Problem for Triangle Graphs
, 1995
"... We show that the Hamiltonian cycle problem is NPcomplete for a class of planar graphs named triangle graphs that are closely related to innertriangulated graphs. We present a lineartime heuristic algorithm that finds a solution at most onethird longer than the optimum solution and use it to obtai ..."
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We show that the Hamiltonian cycle problem is NPcomplete for a class of planar graphs named triangle graphs that are closely related to innertriangulated graphs. We present a lineartime heuristic algorithm that finds a solution at most onethird longer than the optimum solution and use
The Hamiltonian properties of supergrid graphs
, 2015
"... In this paper, we first introduce a novel class of graphs, namely supergrid. Supergrid graphs include grid graphs and triangular grid graphs as their subgraphs. The Hamiltonian cycle and path problems for grid graphs and triangular grid graphs were known to be NPcomplete. However, they are unknown ..."
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In this paper, we first introduce a novel class of graphs, namely supergrid. Supergrid graphs include grid graphs and triangular grid graphs as their subgraphs. The Hamiltonian cycle and path problems for grid graphs and triangular grid graphs were known to be NPcomplete. However, they are unknown
Hamiltonian Paths and Cycles in Planar Graphs
"... Abstract. We examine the problem of counting the number of Hamiltonian paths and Hamiltonian cycles in outerplanar graphs and planar graphs, respectively. We give an O(nαn) upper bound and an Ω(αn) lower bound on the maximum number of Hamiltonian paths in an outerplanar graph with n vertices, wher ..."
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Abstract. We examine the problem of counting the number of Hamiltonian paths and Hamiltonian cycles in outerplanar graphs and planar graphs, respectively. We give an O(nαn) upper bound and an Ω(αn) lower bound on the maximum number of Hamiltonian paths in an outerplanar graph with n vertices
An Algorithm for Finding Hamiltonian Cycles in Grid Graphs Without Holes
, 1996
"... The Hamiltonian cycle problem for general grid graphs is NPcomplete. However, it is conjectured that an efficient algorithm to solve the Hamiltonian cycle problem exists for a subclass of general grid graphs known as grid graphs without holes. This thesis contains a number of results concerning the ..."
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The Hamiltonian cycle problem for general grid graphs is NPcomplete. However, it is conjectured that an efficient algorithm to solve the Hamiltonian cycle problem exists for a subclass of general grid graphs known as grid graphs without holes. This thesis contains a number of results concerning
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