Home  About us  Contact
 

Hamiltonian Graphs (hamiltonian + graph)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

On the construction of combined k -fault-tolerant Hamiltonian graphs

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2001
Chun-Nan Hung
Abstract A graph G is a combined k -fault-tolerant Hamiltonian graph (also called a combined k -Hamiltonian graph) if G , F is Hamiltonian for every subset F , (V(G) , E(G)) with |F| = k. A combined k -Hamiltonian graph G with |V(G)| = n is optimal if it has the minimum number of edges among all n -node k -Hamiltonian graphs. Using the concept of node expansion, we present a powerful construction scheme to construct a larger combined k -Hamiltonian graph from a given smaller graph. Many previous graphs can be constructed by the concept of node expansion. We also show that our construction maintains the optimality property in most cases. The classes of optimal combined k -Hamiltonian graphs that we constructed are shown to have a very good diameter. In particular, those optimal combined 1-Hamiltonian graphs that we constructed have a much smaller diameter than that of those constructed previously by Mukhopadhyaya and Sinha, Harary and Hayes, and Wang et al. © 2001 John Wiley & Sons, Inc. [source]

Independent dominating sets and hamiltonian cycles

JOURNAL OF GRAPH THEORY, Issue 3 2007
Penny Haxell
Abstract A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove that there are no r -regular uniquely hamiltonian graphs when r,>,22. This improves upon earlier results of Thomassen. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 233,244, 2007 [source]

3-colorability of 4-regular hamiltonian graphs,

JOURNAL OF GRAPH THEORY, Issue 2 2003
Herbert Fleischner
Abstract On the model of the cycle-plus-triangles theorem, we consider the problem of 3-colorability of those 4-regular hamiltonian graphs for which the components of the edge-complement of a given hamiltonian cycle are non-selfcrossing cycles of constant length , 4. We show that this problem is NP-complete. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 125,140, 2003 [source]