Bibliographic Details
| Title: |
Computing role assignments of split graphs. |
| Authors: |
Dourado, Mitre Costa1 mitre@dcc.ufrj.br |
| Source: |
Theoretical Computer Science. Jul2016, Vol. 635, p74-84. 11p. |
| Subjects: |
COMSKEE (Computer program language), Graphic methods, Student assignments, Social networks, Algorithms |
| Abstract: |
A k -role assignment of a simple graph G is a surjective function r : V ( G ) → { 1 , … , k } where { r ( u ′ ) : u ′ ∈ N ( u ) } = { r ( v ′ ) : v ′ ∈ N ( v ) } for every pair u , v ∈ V ( G ) with r ( u ) = r ( v ) . This concept appears in the context of social networks. It is known that the problem of finding a 2-role assignment of chordal graphs can be solved in linear time and that deciding whether a graph of this class admits a k -role assignment, for any fixed k ≥ 3 , is NP -complete. In this work, we investigate this problem on split graphs, a subclass of chordal graphs. We characterize the split graphs admitting a 3-role assignment. Such result leads to a linear time algorithm for this case. Furthermore, we prove that deciding whether a split graph has a k -role assignment is NP -complete for any fixed k ≥ 4 . [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
