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 کاملM-alternating Hamilton paths and M-alternating Hamilton cycles
We study M-alternating Hamilton paths, and M-alternating Hamilton cycles in a simple connected graph G on ν vertices with a perfect matchingM . Let G be a bipartite graph, we prove that if for any two vertices x and y in different parts of G, d(x)+d(y) ≥ ν/2+2, then G has an M-alternating Hamilton cycle. For general graphs, a condition for the existence of an M-alternating Hamilton path startin...
متن کاملFamilies of graph-different Hamilton paths
Let D ⊆ N be an arbitrary subset of the natural numbers. For every n, let M(n,D) be the maximum of the cardinality of a set of Hamiltonian paths in the complete graph Kn such that the union of any two paths from the family contains a not necessarily induced cycle of some length from D. We determine or bound the asymptotics of M(n,D) in various special cases. This problem is closely related to t...
متن کاملFamilies of locally separated Hamilton paths
We improve by an exponential factor the lower bound of Körner and Muzi for the cardinality of the largest family of Hamilton paths in a complete graph of n vertices in which the union of any two paths has degree 4. The improvement is through an explicit construction while the previous bound was obtained by a greedy algorithm. We solve a similar problem for permutations up to an exponential factor.
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2017
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2017.2738631