13,133 research outputs found
A Study on Edge-Set Graphs of Certain Graphs
Let be a simple connected graph, with In this
paper, we define an edge-set graph constructed from the graph
such that any vertex of corresponds to the -th
-element subset of and any two vertices of
are adjacent if and only if there is at least one edge in the
edge-subset corresponding to which is adjacent to at least one edge
in the edge-subset corresponding to where are positive
integers. It can be noted that the edge-set graph of a graph
id dependent on both the structure of as well as the number of edges
We also discuss the characteristics and properties of the edge-set
graphs corresponding to certain standard graphs.Comment: 10 pages, 2 figure
Connecting Terminals and 2-Disjoint Connected Subgraphs
Given a graph and a set of terminal vertices we say that a
superset of is -connecting if induces a connected graph, and
is minimal if no strict subset of is -connecting. In this paper we prove
that there are at most minimal -connecting sets when and that
these can be enumerated within a polynomial factor of this bound. This
generalizes the algorithm for enumerating all induced paths between a pair of
vertices, corresponding to the case . We apply our enumeration algorithm
to solve the {\sc 2-Disjoint Connected Subgraphs} problem in time
, improving on the recent algorithm of Cygan et
al. 2012 LATIN paper.Comment: 13 pages, 1 figur
A Polynomial Delay Algorithm for Enumerating Minimal Dominating Sets in Chordal Graphs
An output-polynomial algorithm for the listing of minimal dominating sets in
graphs is a challenging open problem and is known to be equivalent to the
well-known Transversal problem which asks for an output-polynomial algorithm
for listing the set of minimal hitting sets in hypergraphs. We give a
polynomial delay algorithm to list the set of minimal dominating sets in
chordal graphs, an important and well-studied graph class where such an
algorithm was open for a while.Comment: 13 pages, 1 figure, submitte
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