Drawability of Complete Graphs Using a Minimal Slope Set

META-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS

The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...

Graphs with complete minimal k-vertex separators

G. A. Dirac characterized chordal graphs as those in which minimal vertex separators always induce complete subgraphs. I generalize a traditional (2-)vertex separator to a k-vertex separator — meaning a set S of vertices whose removal puts k independent vertices into k separate components. Generalizing Dirac’s theorem, the {P5, 2P3}-free chordal graphs are the graphs in which minimal k-separato...

On set colorings of complete bipartite graphs

In European J. Combin. 30 (2009), 986–995, S.M. Hegde recently introduced set colorings of a graph G as an assignment (function) of distinct subsets of a finite set X of colors to the vertices of G, where the colors of the edges are obtained as the symmetric difference of the sets assigned to their end vertices (which are also distinct). A set coloring is called a proper set coloring if all the...

The Set of Minimal Braids is co-NP-Complete

Braids ñàï Üå represented as two-dimenSional diagrams showing the crossings of strings or as words over the generators of à braid group. À minimal braid is îïå with the fewest crossings (or the shortest words) among all possible repre~entations topologically equivalent to that braid. ÒÜå main result of this paper is that the set of minimal braids is co-NP-complete. Algorithmic problems in braid...

Complete Finite Automata Network Graphs with Minimal Number of Edges