Solving the weighted efficient edge domination problem on bipartite permutation graphs
Discrete Applied Mathematics
A polynomial algorithm to find an independent set of maximum weight in a fork-free graph
Journal of Discrete Algorithms
| Hi-index | 0.89 |
In a graph G=(V,E), an efficient dominating set is a subset D@?V such that D is an independent set such that each vertex outside D has exactly one neighbor in D. E stands for the graph with vertices a,b,c,d,e,f and edges ab,bc,cd,de and cf, while xNet stands for the graph with vertices a,b,c,d,e,f,g and edges ad,be,cf,de,ef,fd and cg. This note shows that, given an (E,xNet)-free graph, a minimum efficient dominating set (if any) can be found in polynomial time, extending two polynomially solvable cases for efficient dominating sets recently found by Milanic (2013) [4], and Brandstadt et al. (2013) [2].