<p>There are plenty of practical applications that depend on graph coloring. For example, <em>Frequency assignment to cellular antennas</em> is a famous problem. In this problem, one can only use small number of frequencies(colors), and assign them to the antennas such that clients always connect to one of the antennas. Problem arises when coverage area of several antennas overlap, and in this case we want to have at least one antenna with unique frequency(color). One cannot use simple <em>proper(non-monotonic)</em> coloring in this problem. </p>

<p>In above case, we deal with <em>colouring of hypergraph</em>. We define hypergraph according to the coloring problem. And there are different variants of colorings, like <em>Conflict-free coloring</em>, <em>Unique-maximum coloring</em>. Many research have been done in case of static situations, where hypergraph do not change over time. And there are many interesting research going on in case of <em>online Setting</em>, where hyper edge may change in time (say some antenna stops working, or new antenna is fixed at some location).</p>

<p>you can also refer <strong><a href="http://arxiv.org/abs/1005.3616" rel="nofollow">1</a></strong> survey paper to read more about interesting coloring problems and its applications.</p>
What is need of graph coloring?
<p>What is the practical application of graph coloring. In other words, why do we need to optimise number of colors(some important feature of a problem) using such algorithms.</p>