Interval incidence coloring of bipartite graphs

In this paper(1) we study the problem of interval incidence coloring of bipartite graphs. We show the upper bound for interval incidence coloring number (chi(ii)) for bipartite graphs chi(ii) <= 2 Delta, and we prove that chi(ii) = 2 Delta holds for regular bipartite graphs. We solve this problem for subcubic bipartite graphs, i.e. we fully characterize the subcubic graphs that admit 4, 5 or 6 coloring, and we construct a linear time exact algorithm for subcubic bipartite graphs. We also study the problem for bipartite graphs with Delta = 4 and we show that 5-coloring is easy and 6-coloring is hard (NP-complete). Moreover, we construct an O(n Delta(3.5) log Delta) time optimal algorithm for trees. (C) 2013 Elsevier B.V. All rights reserved.