منابع مشابه
Hamilton Paths in Grid Graphs
A grid graph is a node-induced finite subgraph of the infinite grid. It is rectangular if its set of nodes is the product of two intervals. Given a rectangular grid graph and two of its nodes, we give necessary and sufficient conditions for the graph to have a Hamilton path between these two nodes. In contrast, the Hamilton path (and circuit) problem for general grid graphs is shown to be NP-co...
متن کاملHamilton paths in toroidal graphs
Tutte has shown that every 4-connected planar graph contains a Hamilton cycle. Grünbaum and Nash-Williams independently conjectured that the same is true for toroidal graphs. In this paper, we prove that every 4-connected toroidal graph contains a Hamilton path. Partially supported by NSF grant DMS-9970514 Partially supported by NSF grants DMS-9970527 and DMS-0245530 Partially supported by RGC ...
متن کاملHamilton Paths in Certain Arithmetic Graphs
For each integer m ≥ 1, consider the graph Gm whose vertex set is the set N = {0, 1, 2, . . . } of natural numbers and whose edges are the pairs xy with y = x + m or y = x − m or y = mx or y = x/m. Our aim in this note is to show that, for each m, the graph Gm contains a Hamilton path. This answers a question of Lichiardopol. For each integer m ≥ 1, consider the graph Gm whose vertex set is the...
متن کاملHamilton paths in generalized Petersen graphs
This thesis puts forward the conjecture that for n > 3k with k > 2, the generalized Petersen graph, GP (n, k) is Hamilton-laceable if n is even and k is odd, and it is Hamilton-connected otherwise. We take the first step in the proof of this conjecture by proving the case n = 3k + 1 and k ≥ 1. We do this mainly by means of an induction which takes us from GP (3k + 1, k) to GP (3(k+2)+1, k+2). T...
متن کاملHamilton Circuits in Hexagonal Grid Graphs
We look at a variant of the Hamilton circuit problem, where the input is restricted to hexagonal grid graphs. A hexagonal grid graph has a vertex set that is a subset of the grid points of a regular hexagonal tiling of the plane and edges corresponding to hexagon sides. We show that Hamilton circuit in hexagonal grid graphs is NP-complete.
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 1982
ISSN: 0097-5397,1095-7111
DOI: 10.1137/0211056