The Depth First Search (DFS) algorithm is one of the basic techniques which is used in a very large variety of graph algorithms. Most applications of the DFS involve the construction of a depth-first spanning tree (DFS tree). In this paper, we give a complete characterization of all the graphs in which every spanning tree is a DFS tree. These graphs are called Total −DFS −Graphs. We prove that ...

Given a degree set D = {a1 < a2 < . . . < an} of nonnegative integers, the minimum number of vertices in any tree realizing the set D is known[10]. In this paper, we study the number of vertices and multiplicity of distinct degrees as parameters of tree realizations of degree sets. We explore this in the context of both directed and undirected trees and asymmetric directed graphs (graphs which ...

Genetic Algorithm-based Quadratic Decision Tree (GA-based QDT) has been applied successfully in various classification problems with non-linear class boundaries. However, the execution time of GA-based QDT is quite long. In this paper, a new version of GA-based QDT, called Genetic Algorithm-based Quadratic Decision Tree with k-D Tree (GA-based QDT with k-D Tree), is proposed. In the proposed al...

K-dimensional trees, abbreviated as k-d trees in the following, are binary search and partitioning trees that represent a set of n points in a multi-dimensional space. K-d tree data structures have primarily been used for nearest neighbor queries and several other query types, for example in database applications. In the context of a research project at the Bauhaus-University Weimar concerned w...

Disjunctive deductive databases (DDDBs) can capture indeenite information, i.e., imprecise or partial knowledge, of the real world. In this paper we present a method for horizontally fragmenting a DDDB based on the minimal-model forest approach. A minimal-model forest of a DDDB D is a collection of minimal-model trees of D such that each tree represents a set of facts that is disjoint from the ...

In 1987, Simonson conjectured that every k-outerplanar graph of the maximum degree d has spanning tree congestion at most k ·d [Math. Syst. Theory 20 (1987) 235–252]. We show that his conjecture is true and the bound is tight for outerplanar graphs and k-outerplanar graphs of maximum degree 4. We give a precise characterization of the spanning tree congestion of outerplanar graphs, and thus sho...

An out-tree T in a digraph D is subgraph of D which is an orientation of a tree that has only one vertex of in-degree 0 (root). A vertex of T is a leaf if it has out-degree 0. A spanning out-tree is called an out-branching. We’ll overview some recent algorithmic and theoretical results on out-branchings with minimum and maximum number of leaves.

A gracious labelling g of a tree is a graceful labelling in which, treating the tree as a bipartite graph, the label of any edge (d,u) (d a ‘down’ and u an ‘up’ vertex) is g(u) – g(d). A gracious k-labelling is one such that each residue class modulo k has the ‘correct’ numbers of vertex and edge labels that is, the numbers that arise by interpreting the labels of a gracious labelling modulo k....

This document denotes the typos in the following paper: N. Ohkura, K. Hirata, T. Kuboyama, M. Harao: The q-Gram Distance for Ordered Unlabeled Trees, Proc. 8th International Conference on Discover Science (DS2005), LNAI, Springer-Verlag, 2005 (to appear). 1 Section 2, the First Paragraph Please replace the first paragraph with the following statements. A tree is a connected graph without cycles...

Consider the nearest neighbor graph for the integer lattice Z in d dimensions. For a large finite piece of it, consider choosing a spanning tree for that piece uniformly among all possible subgraphs that are spanning trees. As the piece gets larger, this approaches a limiting measure on the set of spanning graphs for Z. This is shown to be a tree if and only if d ≤ 4. In this case, the tree has...