On the Kernelization Complexity of Colorful Motifs

The Colorful Motif problem asks if, given a vertex-colored graph G, there exists a subset S of vertices of G such that the graph induced by G on S is connected and contains every color in the graph exactly once. The problem is motivated by applications in computational biology and is also well-studied from the theoretical point of view. In particular, it is known to be NPcomplete even on trees of maximum degree three [Fellows et al, ICALP 2007]. In their pioneering paper that introduced the color-coding technique, Alon et al. [STOC 1995] show, inter alia, that the problem is FPT on general graphs. More recently, Cygan et al. [WG 2010] showed that Colorful Motif is NP-complete on comb graphs, a special subclass of the set of trees of maximum degree three. They also showed that the problem is not likely to admit polynomial kernels on forests. We continue the study of the kernelization complexity of the Colorful Motif problem restricted to simple graph classes. Surprisingly, the infeasibi...

• Type: Journal
• Year: 2010
• Where: IWPEC
• Authors: Abhimanyu M. Ambalath, Radheshyam Balasundaram, Chintan Rao H., Venkata Koppula, Neeldhara Misra, Geevarghese Philip, M. S. Ramanujan
• Keywords: Applied Computing, Colorful Motif, Et Al, IWPEC 2010, Polynomial Kernels