Displaying similar documents to “Balanced aspect ratio trees and their use for drawing large graphs.”

Spanning tree congestion of rook's graphs

Kyohei Kozawa, Yota Otachi (2011)

Discussiones Mathematicae Graph Theory

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Let G be a connected graph and T be a spanning tree of G. For e ∈ E(T), the congestion of e is the number of edges in G joining the two components of T - e. The congestion of T is the maximum congestion over all edges in T. The spanning tree congestion of G is the minimum congestion over all its spanning trees. In this paper, we determine the spanning tree congestion of the rook's graph Kₘ ☐ Kₙ for any m and n.

Programming and Testing a Two-Tree Algorithm

Vassilev, Tzvetalin, Ammerlaan, Joanna (2013)

Serdica Journal of Computing

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ACM Computing Classification System (1998): G.2.2, F.2.2. Recently, Markov, Vassilev and Manev [2] proposed an algorithm for finding the longest path in 2-trees. In this paper, we describe an implementation of the algorithm. We briefly discuss the algorithm and present example that helps the reader grasp the main algorithmic ideas. Further, we discuss the important stages in the implementation of the algorithm and justify the decisions taken. Then, we present experimental...

The color-balanced spanning tree problem

Štefan Berežný, Vladimír Lacko (2005)

Kybernetika

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Suppose a graph G = ( V , E ) whose edges are partitioned into p disjoint categories (colors) is given. In the color-balanced spanning tree problem a spanning tree is looked for that minimizes the variability in the number of edges from different categories. We show that polynomiality of this problem depends on the number p of categories and present some polynomial algorithm.

2-placement of (p,q)-trees

Beata Orchel (2003)

Discussiones Mathematicae Graph Theory

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Let G = (L,R;E) be a bipartite graph such that V(G) = L∪R, |L| = p and |R| = q. G is called (p,q)-tree if G is connected and |E(G)| = p+q-1. Let G = (L,R;E) and H = (L',R';E') be two (p,q)-tree. A bijection f:L ∪ R → L' ∪ R' is said to be a biplacement of G and H if f(L) = L' and f(x)f(y) ∉ E' for every edge xy of G. A biplacement of G and its copy is called 2-placement of G. A bipartite graph G is 2-placeable if G has a 2-placement. In this paper we give all (p,q)-trees...