Computing a 3-role assignment is polynomial-time solvable on complementary prisms
CoRR(2024)
Abstract
A r-role assignment of a simple graph G is an assignment of r distinct
roles to the vertices of G, such that two vertices with the same role have
the same set of roles assigned to related vertices. Furthermore, a specific
r-role assignment defines a role graph, in which the vertices are the
distinct r roles, and there is an edge between two roles whenever there are
two related vertices in the graph G that correspond to these roles. We
consider complementary prisms, which are graphs formed from the disjoint union
of the graph with its respective complement, adding the edges of a perfect
matching between their corresponding vertices. In this work, we characterize
the complementary prisms that do not admit a 3-role assignment. We highlight
that all of them are complementary prisms of disconnected bipartite graphs.
Moreover, using our findings, we show that the problem of deciding whether a
complementary prism has a 3-role assignment can be solved in polynomial time.
MoreTranslated text
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined