SPINNING CATERPILLARS

Universal caterpillars

For a class V of graphs, denote by a(@?) the least value of m so that for some graph II on m vertices, every GE Q occurs as a subgraph of U. In this note we obtain rather sharp bounds on u(q) when Q is the class of caterpillars on n vertices, i.e., tree with property that the vertices of degree exceeding one induce a path. Recently several of the authors have investigated graphs U(g) which are ...

Looping Caterpillars

There are two main paradigms for querying semi structured data: regular path queries and XPath. The aim of this paper is to provide a synthesis between these two. This synthesis is given by a small addition to tree walk automata and the corresponding caterpillar expressions. These are evaluated on unranked finite sibling-ordered trees. At the expression level we add an operator whose meaning is...

Rollercoasters and Caterpillars

A rollercoaster is a sequence of real numbers for which every maximal contiguous subsequence, that is increasing or decreasing, has length at least three. By translating this sequence to a set of points in the plane, a rollercoaster can be defined as a polygonal path for which every maximal sub-path, with positiveor negative-slope edges, has at least three points. Given a sequence of distinct r...

Caterpillars and polymorphisms.

Constructing Graceful Graphs with Caterpillars

A graceful labeling of a graph G of size n is an injective assignment of integers from {0, 1,..., n} to the vertices of G, such that when each edge of G has assigned a weight, given by the absolute dierence of the labels of its end vertices, the set of weights is {1, 2,..., n}. If a graceful labeling f of a bipartite graph G assigns the smaller labels to one of the two stable sets of G, then f ...