Bicubic maps are in bijection with (0 ; 1)-trees. We introduce two new ways of decomposing (0 ; 1)-trees. Using this we de ne an endofunc- tion on (0 ; 1)-trees, and thus also on bicubic maps. We show that ...

This paper deals with the question of completing a monotone increasing family of subsets Gamma of a finite set Omega to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we prove ...

This paper studies structural aspects of lattice path matroids. Among the basic topics treated are direct sums, duals, minors, circuits, and connected flats. One of the main results is a characterization of lattice path ...

The main result of this paper is the introduction of marked graphs and the marked graph polynomials ( -polynomial) associated with them. These polynomials can be defined via a deletion-contraction operation. These polynomials ...