Loading...
Search for:
not-all-equal-3-sat
0.011 seconds
On the Complexity of Deciding Whether the Regular Number is at Most Two
, Article Graphs and Combinatorics ; Volume 31, Issue 5 , September , 2014 , pp 1359-1365 ; ISSN: 09110119 ; Sadeghi, M. R ; Ahadi, A ; Sharif University of Technology
Abstract
The regular number of a graph (Formula presented.) denoted by (Formula presented.) is the minimum number of subsets into which the edge set of (Formula presented.) can be partitioned so that the subgraph induced by each subset is regular. In this work we answer to the problem posed as an open problem in Ganesan et al. (J Discrete Math Sci Cryptogr 15(2-3):49-157, 2012) about the complexity of determining the regular number of graphs. We show that computation of the regular number for connected bipartite graphs is NP-hard. Furthermore, we show that, determining whether (Formula presented.) for a given connected (Formula presented.)-colorable graph (Formula presented.) is NP-complete. Also, we...