Pattern Recognition and Image Processing Group Institute of Computer Aided Automation Vienna University of Technology Treitlstr. 3/1832 A-1040 Vienna AUSTRIA Phone: +43 (1) 58801-18351 Fax: +43 (1) 5054668 E-mail: [email protected], [email protected] URL: http://www.prip.tuwien.ac.at/ PRIP-TR-54 January 29, 1999 Dual Contraction of Combinatorial Maps Luc Brun and Walter Kropatsch1 Abs...

For any graph G with fixed boundary there exists a layout in the plane, which minimizes the maximum Euclidean distance of any node to its neighbors. This layout balances the length of the graph edges and is therefore called a (length-) balanced layout of G. Furthermore the existence of a unique optimal balanced layout L with the following properties is proved: (i) L is the minimal element of an...

An unweighted, connected graph is distance-balanced (also called self-median) if there exists a number d such that, for any vertex v, the sum of the distances from v to all other vertices is d. An unweighted connected graph is strongly distancebalanced (also called distance-degree regular) if there exist numbers d1, d2, d3, . . . such that, for any vertex v, there are precisely dk vertices at d...

A hole in a graph is an induced cycle on at least four vertices. A graph is Berge if it has no odd hole and if its complement has no odd hole. In 2002, Chudnovsky, Robertson, Seymour and Thomas proved a decomposition theorem for Berge graphs saying that every Berge graph either is in a well understood basic class or has some kind of decomposition. Then, Chudnovsky proved stronger theorems. One ...

A celebrated theorem of Savitch [Sav70] states that NSPACE(S) ⊆ DSPACE(S). In particular, Savitch gave a deterministic algorithm to solve ST-CONNECTIVITY (an NL-complete problem) using O(logn) space, implying NL ⊆ DSPACE(logn). While Savitch’s theorem itself has not been improved in the last four decades, studying the space complexity of several special cases of STCONNECTIVITY has provided new ...

An undirected simple graphG is locally irregular if adjacent vertices ofG have different degrees. An edge-colouring φ ofG is locally irregular if each colour class of φ induces a locally irregular subgraph of G. The irregular chromatic index χirr(G) of G is the least number of colours used by a locally irregular edge-colouring of G (if any). We show that the problem of determining the irregular...

Locality behavior study is crucial for achieving good performance for irregular problems. Graph algorithms with large, sparse inputs, for example, oftentimes achieve only a tiny fraction of the potential peak performance on current architectures. Compared with most numerical algorithms graph algorithms lay higher pressure on the memory system. In this paper, using the minimum spanning tree prob...

We introduce and study balanced online graph avoidance games on the random graph process. The game is played by a player we call Painter. Edges of the complete graph with n vertices are revealed two at a time in a random order. In each move, Painter immediately and irrevocably decides on a balanced coloring of the new edge pair: either the first edge is colored red and the second one blue or vi...

Quasi-random graphs can be informally described as graphs whose edge distribution closely resembles that of a truly random graph of the same edge density. Recently, Shapira and Yuster proved the following result on quasi-randomness of graphs. Let k ≥ 2 be a fixed integer, α1, . . . , αk be positive reals satisfying ∑ i αi = 1 and (α1, . . . , αk) 6= (1/k, . . . , 1/k), and G be a graph on n ver...

A graph G is strongly distance-balanced if for every edge uv of G and every i ≥ 0 the number of vertices x with d(x, u) = d(x, v)−1 = i equals the number of vertices y with d(y, v) = d(y, u) − 1 = i. It is proved that the strong product of graphs is strongly distance-balanced if and only if both factors are strongly distancebalanced. It is also proved that connected components of the direct pro...