Enumeration of Hamiltonian cycles on a thick grid cylinder - part I: Non-contractible Hamiltonian cycles
نویسندگان
چکیده
منابع مشابه
Contractible Hamiltonian Cycles in Triangulated Surfaces
A triangulation of a surface is called q-equivelar if each of its vertices is incident with exactly q triangles. In 1972 Altshuler had shown that an equivelar triangulation of torus has a Hamiltonian Circuit. Here we present a necessary and sufficient condition for existence of a contractible Hamiltonian Cycle in equivelar triangulation of a surface. AMS classification : 57Q15, 57M20, 57N05.
متن کاملContractible Hamiltonian cycles in Polyhedral Maps
We present a necessary and sufficient condition for existence of a contractible Hamiltonian Cycle in the edge graph of equivelar maps on surfaces. We also present an algorithm to construct such cycles. This is further generalized and shown to hold for more general maps. AMS classification : 57Q15, 57M20, 57N05.
متن کاملEnumeration of Hamiltonian Cycles in 6-cube
Finding the number 2H6 of directed Hamiltonian cycles in 6-cube is problem 43 in Section 7.2.1.1 of Knuth’s The Art of Computer Programming ([Kn10]); various proposed estimates are surveyed below. We computed exact value: H6=14, 754, 666, 508, 334, 433, 250, 560=6!*2 4*217, 199*1, 085, 989*5, 429, 923. Also the number Aut6 of those cycles up to automorphisms of 6-cube was computed as 147,365,40...
متن کاملA Conjecture on the Number of Hamiltonian Cycles on Thin Grid Cylinder Graphs
We study the enumeration of Hamiltonian cycles on the thin grid cylinder graph Cm × Pn+1. We distinguish two types of Hamiltonian cycles depending on their contractibility (as Jordan curves) and denote their numbers h m (n) and hm(n). For fixedm, both of them satisfy linear homogeneous recurrence relations with constant coefficients. We derive their generating functions and other related result...
متن کاملOn Hamiltonian cycles and Hamiltonian paths
A Hamiltonian cycle is a spanning cycle in a graph, i.e., a cycle through every vertex, and a Hamiltonian path is a spanning path. In this paper we present two theorems stating sufficient conditions for a graph to possess Hamiltonian cycles and Hamiltonian paths. The significance of the theorems is discussed, and it is shown that the famous Ore’s theorem directly follows from our result. 2004...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applicable Analysis and Discrete Mathematics
سال: 2019
ISSN: 1452-8630,2406-100X
DOI: 10.2298/aadm171215025b