The interval number of a complete multipartite graph

The interval number of a complete multipartite graph

The interval number of a graph G, denoted i(G), is the least positive integer t for which G is the intersection graph of a family of sets each of which is the union of at most t cIosed intervals of the real line IR. Trotter and Harary showed that the interval number of the complete bipartite graph K(m, n) is [(mn + I)/(m + n)]. Matthews showed that the interval number of the complete multiparti...

Heterochromatic tree partition number of a complete multipartite graph

A heterochromatic tree is an edge-colored tree in which any two edges have different colors. The heterochromatic tree partition number of an r-edge-colored graph G, denoted by tr(G), is the minimum k such that whenever the edges of the graph G are colored with r colors, the vertices of G can be covered by at most k vertexdisjoint heterochromatic trees. In this paper we determine the heterochrom...

Interval colorings of complete balanced multipartite graphs

A graph G is called a complete k-partite (k ≥ 2) graph if its vertices can be partitioned into k independent sets V1, . . . , Vk such that each vertex in Vi is adjacent to all the other vertices in Vj for 1 ≤ i < j ≤ k. A complete k-partite graph G is a complete balanced kpartite graph if |V1| = |V2| = · · · = |Vk|. An edge-coloring of a graph G with colors 1, . . . , t is an interval t-colorin...

The diameter of an orientation of a complete multipartite graph

Fault Tolerant Routings in Complete Multipartite Graph

The f -tolerant arc-forwarding index for a class of complete multipartite graphs are determined by constructing relevant fault tolerant routings. Furthermore, these routings are leveled for Cocktail-party graph and the complete 3-partite graph. Mathematics Subject Classification: 05C38, 05C90, 90B10