A supergrid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional supergrid. The supergrid graphs contain grid graphs and triangular grid graphs as subgraphs. The Hamiltonian cycle problem for grid and triangular grid graphs was known to be NP-complete. In the past, we have shown that the Hamiltonian cycle problem for supergrid graphs is also NP-complete. ...

Let G be a simple connected graph of order n. A hamiltonian coloring c of a graph G is an assignment of colors (non-negative integers) to the vertices of G such that D(u, v) + |c(u) − c(v)| ≥ n − 1 for every two distinct vertices u and v of G, where D(u, v) denotes the detour distance between u and v in G which is the length of the longest path between u and v. The value hc(c) of a hamiltonian ...

Example 1 Undirected Hamiltonian Path (UHP) and Undirected Hamiltonian Circuit (UHC) are the same problems as the corresponding problems for directed graphs, but the new problems are for undirected graphs. Claim 2 Given a polynomial time algorithm for Undirected Hamiltonian Path (UHP) there is a polynomial time algorithm for Directed Hamiltonian Path. 1. A DHP builds the triple (H, p, q), where...

Abstract. An upper bound for the number of Hamiltonian cycles of symmetric diagraphs is established first in this paper, which is tighter than the famous Minc’s bound and the Brégman’s bound. A transformation on graphs is proposed, so that counting the number of Hamiltonian cycles of an undirected graph can be done by counting the number of Hamiltonian cycles of its corresponding symmetric dire...

The complete double vertex graph $M_2(G)$ of $G$ is defined as the whose vertices are $2$-multisubsets $V(G)$, and two such adjacent in if their symmetric difference (as multisets) a pair $G$. In this paper we exhibit an infinite family graphs (containing Hamiltonian non-Hamiltonian graphs) for which Hamiltonian.

Graphs can be used to model various problems and relations in diverse domains eg. Computer Science, Biological, Chemical and many other. There exist various hard problems in communication networks, which are practically hard but can be shaped in the form of graphs. A Hamiltonian Path is a spanning trail in a network graph i.e. a path through every network node and a spanning cycle in a network ...

A Hamiltonian cycle in a graph G is a simple cycle in which each vertex of G appears exactly once. The Hamiltonian cycle problem involves testing whether a Hamiltonian cycle exists in a graph, and finds one if such a cycle does exist. It is well known that the Hamiltonian cycle problem is one of the classic NP-complete problems on general graphs. Shih et al. solved the Hamiltonian cycle problem...

In this paper, we give the necessary and sufficient conditions for the existence of Hamiltonian paths in L−alphabet and C−alphabet grid graphs. We also present a linear-time algorithm for finding Hamiltonian paths in these graphs.

A simple graph G is k-ordered (respectively, k-ordered hamiltonian) if, for any sequence of k distinct vertices v1, . . . , vk of G, there exists a cycle (respectively, a hamiltonian cycle) in G containing these k vertices in the specified order. In 1997 Ng and Schultz introduced these concepts of cycle orderability, and motivated by the fact that k-orderedness of a graph implies (k − 1)-connec...

We describe some necessary conditions for the existence of a Hamiltonian path in any graph (in other words, for a graph to be traceable). These conditions result in a linear time algorithm to decide the Hamiltonian path problem for cactus graphs. We apply this algorithm to several molecular databases to report the numbers of graphs that are traceable cactus graphs.