95 research outputs found
Recognizing clique graphs of directed and rooted path graphs
AbstractWe describe characterizations for the classes of clique graphs of directed and rooted path graphs. The characterizations relate these classes to those of clique-Helly and strongly chordal graphs, respectively, which properly contain them. The characterizations lead to polynomial time algorithms for recognizing graphs of these classes
Efficient and Perfect domination on circular-arc graphs
Given a graph , a \emph{perfect dominating set} is a subset of
vertices such that each vertex is
dominated by exactly one vertex . An \emph{efficient dominating set}
is a perfect dominating set where is also an independent set. These
problems are usually posed in terms of edges instead of vertices. Both
problems, either for the vertex or edge variant, remains NP-Hard, even when
restricted to certain graphs families. We study both variants of the problems
for the circular-arc graphs, and show efficient algorithms for all of them
Even and odd pairs in comparability and in P4-comparability graphs
AbstractWe characterize even and odd pairs in comparability and in P4-comparability graphs. The characterizations lead to simple algorithms for deciding whether a given pair of vertices forms an even or odd pair in these classes of graphs. The complexities of the proposed algorithms are O(n + m) for comparability graphs and O(n2m) for P4-comparability graphs. The former represents an improvement over a recent algorithm of complexity O(nm)
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