158 research outputs found
Rainbow domination and related problems on some classes of perfect graphs
Let and let be a graph. A function is a rainbow function if, for every vertex with
, . The rainbow domination number
is the minimum of over all rainbow
functions. We investigate the rainbow domination problem for some classes of
perfect graphs
On the stable degree of graphs
We define the stable degree s(G) of a graph G by s(G)∈=∈ min max d (v), where the minimum is taken over all maximal independent sets U of G. For this new parameter we prove the following. Deciding whether a graph has stable degree at most k is NP-complete for every fixed k∈≥∈3; and the stable degree is hard to approximate. For asteroidal triple-free graphs and graphs of bounded asteroidal number the stable degree can be computed in polynomial time. For graphs in these classes the treewidth is bounded from below and above in terms of the stable degree
Space Efficient Algorithms for Breadth-Depth Search
Continuing the recent trend, in this article we design several
space-efficient algorithms for two well-known graph search methods. Both these
search methods share the same name {\it breadth-depth search} (henceforth {\sf
BDS}), although they work entirely in different fashion. The classical
implementation for these graph search methods takes time and bits of space in the standard word RAM model (with word size being
bits), where and denotes the number of edges and
vertices of the input graph respectively. Our goal here is to beat the space
bound of the classical implementations, and design space
algorithms for these search methods by paying little to no penalty in the
running time. Note that our space bounds (i.e., with bits of
space) do not even allow us to explicitly store the required information to
implement the classical algorithms, yet our algorithms visits and reports all
the vertices of the input graph in correct order.Comment: 12 pages, This work will appear in FCT 201
Line-distortion, Bandwidth and Path-length of a graph
We investigate the minimum line-distortion and the minimum bandwidth problems
on unweighted graphs and their relations with the minimum length of a
Robertson-Seymour's path-decomposition. The length of a path-decomposition of a
graph is the largest diameter of a bag in the decomposition. The path-length of
a graph is the minimum length over all its path-decompositions. In particular,
we show:
- if a graph can be embedded into the line with distortion , then
admits a Robertson-Seymour's path-decomposition with bags of diameter at most
in ;
- for every class of graphs with path-length bounded by a constant, there
exist an efficient constant-factor approximation algorithm for the minimum
line-distortion problem and an efficient constant-factor approximation
algorithm for the minimum bandwidth problem;
- there is an efficient 2-approximation algorithm for computing the
path-length of an arbitrary graph;
- AT-free graphs and some intersection families of graphs have path-length at
most 2;
- for AT-free graphs, there exist a linear time 8-approximation algorithm for
the minimum line-distortion problem and a linear time 4-approximation algorithm
for the minimum bandwidth problem
On retracts, absolute retracts, and folds in cographs
Let G and H be two cographs. We show that the problem to determine whether H
is a retract of G is NP-complete. We show that this problem is fixed-parameter
tractable when parameterized by the size of H. When restricted to the class of
threshold graphs or to the class of trivially perfect graphs, the problem
becomes tractable in polynomial time. The problem is also soluble when one
cograph is given as an induced subgraph of the other. We characterize absolute
retracts of cographs.Comment: 15 page
Independent Set Reconfiguration in Cographs
We study the following independent set reconfiguration problem, called
TAR-Reachability: given two independent sets and of a graph , both
of size at least , is it possible to transform into by adding and
removing vertices one-by-one, while maintaining an independent set of size at
least throughout? This problem is known to be PSPACE-hard in general. For
the case that is a cograph (i.e. -free graph) on vertices, we show
that it can be solved in time , and that the length of a shortest
reconfiguration sequence from to is bounded by , if such a
sequence exists.
More generally, we show that if is a graph class for which (i)
TAR-Reachability can be solved efficiently, (ii) maximum independent sets can
be computed efficiently, and which satisfies a certain additional property,
then the problem can be solved efficiently for any graph that can be obtained
from a collection of graphs in using disjoint union and complete join
operations. Chordal graphs are given as an example of such a class
Parameterized Edge Hamiltonicity
We study the parameterized complexity of the classical Edge Hamiltonian Path
problem and give several fixed-parameter tractability results. First, we settle
an open question of Demaine et al. by showing that Edge Hamiltonian Path is FPT
parameterized by vertex cover, and that it also admits a cubic kernel. We then
show fixed-parameter tractability even for a generalization of the problem to
arbitrary hypergraphs, parameterized by the size of a (supplied) hitting set.
We also consider the problem parameterized by treewidth or clique-width.
Surprisingly, we show that the problem is FPT for both of these standard
parameters, in contrast to its vertex version, which is W-hard for
clique-width. Our technique, which may be of independent interest, relies on a
structural characterization of clique-width in terms of treewidth and complete
bipartite subgraphs due to Gurski and Wanke
Analysing participatory video through the capability approach. A case study in Quart de Poblet (Valencia, Spain)
The aim of this paper is to analyse participatory video as a participatory action research method through the lenses of the capability approach. In order to do this, we used a participatory video experience that took place in the municipality of Quart de Poblet (Valencia, Spain) from February to March 2014. The participants were 11 young people between 16 and 24 years of age, severely affected by the economic crisis that has hit Spain in recent years. To develop our analysis, we introduced the participatory video as a technique and a process within the participatory action research methods. Then, we analysed the participatory process to verify the extent to which it had contributed to expanding the capabilities and agency of the participants. The evidence revealed a significant expansion of the awareness capability and, in some cases, of the capability for voice. In contrast, the capability to aspire and the agency of the participants were not expanded, due to contextual factors and the limitations of the process itself
Fully dynamic recognition of proper circular-arc graphs
We present a fully dynamic algorithm for the recognition of proper
circular-arc (PCA) graphs. The allowed operations on the graph involve the
insertion and removal of vertices (together with its incident edges) or edges.
Edge operations cost O(log n) time, where n is the number of vertices of the
graph, while vertex operations cost O(log n + d) time, where d is the degree of
the modified vertex. We also show incremental and decremental algorithms that
work in O(1) time per inserted or removed edge. As part of our algorithm, fully
dynamic connectivity and co-connectivity algorithms that work in O(log n) time
per operation are obtained. Also, an O(\Delta) time algorithm for determining
if a PCA representation corresponds to a co-bipartite graph is provided, where
\Delta\ is the maximum among the degrees of the vertices. When the graph is
co-bipartite, a co-bipartition of each of its co-components is obtained within
the same amount of time.Comment: 60 pages, 15 figure
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