Precoloring Extension (PrExt) for Interval Graphs

Motivated by the ‘Precoloring Extension I. Interval Graphs’ in a series devoted to the study of the following general problem on vertex colorings of graph, “suppose that some vertices of a graph G are assigned to some colors, can this precoloring be extended to a proper coloring of G with at most k colors for some given k?”, this work deals with precoloring for sub graphs of interval graphs. The complexity status of precoloring for interval graphs is investigated. . The work has been extended to precoloring to interval graphs with vertices n = 6. Both extendable and non-extendable interval graphs are investigated and conclusions are arrived.