NICNET - a Hierarchic distributed computer-communication network for decision support in the Indian Government

A decision support information system for the Indian Government is being evolved, based on the design of a predominantly query-based computer network with hierarchric distributed databases and random access communication. The four level hierarchy spans 439 districts at the lowest level, the Central Government headquarters in New Delhi, the set of 32 State Capitals and Union Territories, and the set of four Regional Centres. With interference tolerance and random access as two guiding principles behind the choice, Spread Spectrum transmission and Code Division Multiple Access system of satellite communication was adopted. Each node of the network is a 32-bit computer which is capable of local bulk storage of up to three units of 300 megabytes each for purposes of queryaccessible distributed databases. The design and implementation of such a distributed database has endowed the network with the capability to distribute the data related to such databases over various nodes in the network so as to be able to accept a query from any of the nodes

Total coloring of 1-toroidal graphs of maximum degree at least 11 and no adjacent triangles

A {\em total coloring} of a graph $G$ is an assignment of colors to the vertices and the edges of $G$ such that every pair of adjacent/incident elements receive distinct colors. The {\em total chromatic number} of a graph $G$, denoted by \chiup''(G), is the minimum number of colors in a total coloring of $G$. The well-known Total Coloring Conjecture (TCC) says that every graph with maximum degree $\Delta$ admits a total coloring with at most $\Delta + 2$ colors. A graph is {\em $1$-toroidal} if it can be drawn in torus such that every edge crosses at most one other edge. In this paper, we investigate the total coloring of $1$-toroidal graphs, and prove that the TCC holds for the $1$-toroidal graphs with maximum degree at least~$11$ and some restrictions on the triangles. Consequently, if $G$ is a $1$-toroidal graph with maximum degree $\Delta$ at least~$11$ and without adjacent triangles, then $G$ admits a total coloring with at most $\Delta + 2$ colors.Comment: 10 page

National Informatics Centre

175-17

Coloring Algorithms on Subcubic Graphs

We present efficient algorithms for three coloring problems on subcubic graphs (ones with maximum degree 3). These algorithms are based on a simple decomposition principle for subcubic graphs. The first algorithm is for 4-edge coloring, or more generally, 4-list-edge coloring