Multidimensional bipartite trees

Representing Multidimensional Trees

This paper develops a formal definition of multidimensional trees as abstract structures in “left-child, right-sibling” form. After developing this abstract definition, we show how it can be directly implemented as an ADT suitable for use in parsing applications. Additionally, we show how, when viewed in a slightly different way, our definition yields a flat form suitable for serialized input a...

Multidimensional Balanced Binary Trees

A bstract-A new balanced multidimensional tree structure called a k-dimensional balanced binary tree, k a positive integer, is presented and investigated. It is shown that the data structure can be used to manage a set of n k-dimensional data items such that access, insertion, and deletion operations can be supported in Ooog n + k) time. The data structure is a multidimensional generalization o...

Spanning $k$-trees of Bipartite Graphs

A tree is called a k-tree if its maximum degree is at most k. We prove the following theorem. Let k ⩾ 2 be an integer, and G be a connected bipartite graph with bipartition (A,B) such that |A| ⩽ |B| ⩽ (k − 1)|A| + 1. If σk(G) ⩾ |B|, then G has a spanning k-tree, where σk(G) denotes the minimum degree sum of k independent vertices of G. Moreover, the condition on σk(G) is sharp. It was shown by ...

Bipartite Embeddings of Trees in the Plane

Given a tree T on n vertices and a set P of n points in the plane in general position, it is known that T can be straight line embedded in P without crossings. The problem becomes more diicult if T is rooted and we want to root it at any particular point of P. The problem in this form was posed by Perles and partially solved by Pach and Torosick 5]. A complete solution was found by Ikebe et al....

Bipartite graphs with even spanning trees