On the choice number of complete multipartite graphs with part size four

On graphs with complete multipartite µ-graphs

On-Line Choice Number of Complete Multipartite Graphs: an Algorithmic Approach

This paper studies the on-line choice number of complete multipartite graphs with independence number m. We give a unified strategy for every prescribed m. Our main result leads to several interesting consequences comparable to known results. (1) If k1− m ∑ p=2 ( p2 2 − 3p 2 + 1 ) kp > 0, where kp denotes the number of parts of cardinality p, then G is on-line chromatic-choosable. (2) If |V (G)...

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 ...

The p-domination number of complete multipartite graphs

Integral complete multipartite graphs

A graph is called integral if all eigenvalues of its adjacency matrix are integers. In this paper, we investigate integral complete r-partite graphsKp1,p2,...,pr =Ka1·p1,a2·p2,...,as ·ps with s=3, 4.We can construct infinite many new classes of such integral graphs by solving some certain Diophantine equations. These results are different from those in the existing literature. For s = 4, we giv...