5 research outputs found
Hamilton paths in Z-transformation graphs of perfect matchings of hexagonal systems
AbstractLet H be a hexagonal system. The Z-transformation graph Z(H) is the graph where the vertices are the perfect matchings of H and where two perfect matchings are joined by an edge provided their symmetric difference is a hexagon of H (Z. Fu-ji et al., 1988). In this paper we prove that Z(H) has a Hamilton path if H is a catacondensed hexagonal system
Graphs of non-crossing perfect matchings
Let Pn be a set of n = 2m points that are the vertices of a convex polygon, and let Mm
be the graph having as vertices all the perfect matchings in the point set Pn whose edges
are straight line segments and do not cross, and edges joining two perfect matchings M1
and M2 if M2 = M1 ¡ (a; b) ¡ (c; d) + (a; d) + (b; c) for some points a; b; c; d of Pn. We
prove the following results about Mm: its diameter is m ¡ 1; it is bipartite for every m;
the connectivity is equal to m ¡ 1; it has no Hamilton path for m odd, m > 3; and finally
it has a Hamilton cycle for every m even, m>=4
Hamilton paths in Z-transformation graphs of perfect matchings of hexagonal systems
Let H be a hexagonal system. The Z-transformation graph Z(H) is the graph where the vertices are the perfect matchings of H and where two perfect matchings are joined by an edge provided their symmetric difference is a hexagon of H (Z. Fu-ji et al., 1988). In this paper we prove that Z(H) has a Hamilton path if H is a catacondensed hexagonal system