Abstract
For graph classes \wp_1,...,\wp_k, Generalized Graph Coloring is the problem of deciding whether the vertex set of a given graph G can be partitioned into subsets V_1,...,V_k so that V_j induces a graph in the class \wp_j (j=1,2,...,k). If \wp_1=...=\wp_k is the class of edgeless graphs, then this problem coincides with the standard vertex k-COLORABILITY, which is known to be NP-complete for any k≥ 3. Recently, this result has been generalized by showing that if all \wp_i's are additive hereditary, then the generalized graph coloring is NP-hard, with the only exception of bipartite graphs. Clearly, a similar result follows when all the \wp_i's are co-additive.
Highlights
All graphs in this paper are finite, without loops and multiple edges
We say that a graph G is H-free if G does not contain H as an induced subgraph
We study the problem under the assumption that both P - and Q -RECOGNITION are polynomial-time solvable and present infinitely many classes of (P, Q )-colorable graphs with polynomial recognition time. These two results together give a complete answer to the question of complexity of (P ◦ Q )-RECOGNITION when P and Q are additive monotone
Summary
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. If P1 = · · · = Pk is the class of edgeless graphs, this problem coincides with the standard vertex k-COLORABILITY, which is known to be NP-complete for any k ≥ 3. This result has been generalized by showing that if all Pi’s are additive hereditary, the generalized graph coloring is NP-hard, with the only exception of bipartite graphs. We study the problem where we have a mixture of additive and co-additive classes, presenting several new results dealing both with NP-hard and polynomial-time solvable instances of the problem
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Discrete Mathematics & Theoretical Computer Science
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
