Non-Hamiltonian Holes in Grid Graphs

Computer Science – Discrete Mathematics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

10 pages, 8 figures

Scientific paper

In this paper we extend general grid graphs to the grid graphs consist of polygons tiling on a plane, named polygonal grid graphs. With a cycle basis satisfied polygons tiling, we study the cyclic structure of Hamilton graphs. A Hamilton cycle can be expressed as a symmetric difference of a subset of cycles in the basis. From the combinatorial relations of vertices in the subset of cycles in the basis, we deduce the formula of inside faces in Grinberg theorem, called Grinberg equation, and derive a kind of cycles whose existence make a polygonal grid graph non-Hamiltonian, called non-Hamiltonian holes, and then we characterize the existence condition of non-Hamiltonian holes and obtain the necessary and sufficient condition of a polygonal grid graph to be Hamiltonian. The result in this paper provides a new starting point for developing a polynomial-time algorithm for Hamilton problem in general grid graphs.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Non-Hamiltonian Holes in Grid Graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Non-Hamiltonian Holes in Grid Graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-Hamiltonian Holes in Grid Graphs will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-519234

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.