305 research outputs found
An Upper Bound on the Size of Obstructions for Bounded Linear Rank-Width
We provide a doubly exponential upper bound in on the size of forbidden
pivot-minors for symmetric or skew-symmetric matrices over a fixed finite field
of linear rank-width at most . As a corollary, we obtain a
doubly exponential upper bound in on the size of forbidden vertex-minors
for graphs of linear rank-width at most . This solves an open question
raised by Jeong, Kwon, and Oum [Excluded vertex-minors for graphs of linear
rank-width at most . European J. Combin., 41:242--257, 2014]. We also give a
doubly exponential upper bound in on the size of forbidden minors for
matroids representable over a fixed finite field of path-width at most .
Our basic tool is the pseudo-minor order used by Lagergren [Upper Bounds on
the Size of Obstructions and Interwines, Journal of Combinatorial Theory Series
B, 73:7--40, 1998] to bound the size of forbidden graph minors for bounded
path-width. To adapt this notion into linear rank-width, it is necessary to
well define partial pieces of graphs and merging operations that fit to
pivot-minors. Using the algebraic operations introduced by Courcelle and
Kant\'e, and then extended to (skew-)symmetric matrices by Kant\'e and Rao, we
define boundaried -labelled graphs and prove similar structure theorems for
pivot-minor and linear rank-width.Comment: 28 pages, 1 figur
Linear rank-width of distance-hereditary graphs II. Vertex-minor obstructions
In the companion paper [Linear rank-width of distance-hereditary graphs I. A
polynomial-time algorithm, Algorithmica 78(1):342--377, 2017], we presented a
characterization of the linear rank-width of distance-hereditary graphs, from
which we derived an algorithm to compute it in polynomial time. In this paper,
we investigate structural properties of distance-hereditary graphs based on
this characterization.
First, we prove that for a fixed tree , every distance-hereditary graph of
sufficiently large linear rank-width contains a vertex-minor isomorphic to .
We extend this property to bigger graph classes, namely, classes of graphs
whose prime induced subgraphs have bounded linear rank-width. Here, prime
graphs are graphs containing no splits. We conjecture that for every tree ,
every graph of sufficiently large linear rank-width contains a vertex-minor
isomorphic to . Our result implies that it is sufficient to prove this
conjecture for prime graphs.
For a class of graphs closed under taking vertex-minors, a graph
is called a vertex-minor obstruction for if but all of
its proper vertex-minors are contained in . Secondly, we provide, for
each , a set of distance-hereditary graphs that contains all
distance-hereditary vertex-minor obstructions for graphs of linear rank-width
at most . Also, we give a simpler way to obtain the known vertex-minor
obstructions for graphs of linear rank-width at most .Comment: 38 pages, 13 figures, 1 table, revised journal version. A preliminary
version of Section 5 appeared in the proceedings of WG1
Linear rank-width of distance-hereditary graphs I. A polynomial-time algorithm
Linear rank-width is a linearized variation of rank-width, and it is deeply
related to matroid path-width. In this paper, we show that the linear
rank-width of every -vertex distance-hereditary graph, equivalently a graph
of rank-width at most , can be computed in time , and a linear layout witnessing the linear rank-width can be computed with
the same time complexity. As a corollary, we show that the path-width of every
-element matroid of branch-width at most can be computed in time
, provided that the matroid is given by an
independent set oracle.
To establish this result, we present a characterization of the linear
rank-width of distance-hereditary graphs in terms of their canonical split
decompositions. This characterization is similar to the known characterization
of the path-width of forests given by Ellis, Sudborough, and Turner [The vertex
separation and search number of a graph. Inf. Comput., 113(1):50--79, 1994].
However, different from forests, it is non-trivial to relate substructures of
the canonical split decomposition of a graph with some substructures of the
given graph. We introduce a notion of `limbs' of canonical split
decompositions, which correspond to certain vertex-minors of the original
graph, for the right characterization.Comment: 28 pages, 3 figures, 2 table. A preliminary version appeared in the
proceedings of WG'1
An FPT algorithm and a polynomial kernel for Linear Rankwidth-1 Vertex Deletion
Linear rankwidth is a linearized variant of rankwidth, introduced by Oum and
Seymour [Approximating clique-width and branch-width. J. Combin. Theory Ser. B,
96(4):514--528, 2006]. Motivated from recent development on graph modification
problems regarding classes of graphs of bounded treewidth or pathwidth, we
study the Linear Rankwidth-1 Vertex Deletion problem (shortly, LRW1-Vertex
Deletion). In the LRW1-Vertex Deletion problem, given an -vertex graph
and a positive integer , we want to decide whether there is a set of at most
vertices whose removal turns into a graph of linear rankwidth at most
and find such a vertex set if one exists. While the meta-theorem of
Courcelle, Makowsky, and Rotics implies that LRW1-Vertex Deletion can be solved
in time for some function , it is not clear whether this
problem allows a running time with a modest exponential function.
We first establish that LRW1-Vertex Deletion can be solved in time . The major obstacle to this end is how to handle a long
induced cycle as an obstruction. To fix this issue, we define necklace graphs
and investigate their structural properties. Later, we reduce the polynomial
factor by refining the trivial branching step based on a cliquewidth expression
of a graph, and obtain an algorithm that runs in time . We also prove that the running time cannot be improved to under the Exponential Time Hypothesis assumption. Lastly,
we show that the LRW1-Vertex Deletion problem admits a polynomial kernel.Comment: 29 pages, 9 figures, An extended abstract appeared in IPEC201
Modulation of Immune Response in Lambs
Experiments using different types of antigen-adjuvant preparations were conducted in outbred sheep to compare effects of adjuvants on immune responses. Trinitrophenyl-ovalbumin (TNP-ovalbumin) incorporated in a preparation with nonionic block copolymers elicited high antibody titers to both ovalbumin and TNP. Different humoral immune responses were observed when Pasteurella haemolytica lipopolysaccharide (LPS) was added to the preparations. Responses to ovalbumin and TNP were reduced when Pasteurella haemolytica LPS was added to copolymer L121. The antibody titers to ovalbumin or TNP were not affected by the addition of LPS to the preparation containing copolymer L180.5. Lymphocyte proliferation assays demonstrated high stimulation indices at day 17 to ovalbumin by lymphocytes from lambs receiving preparations containing copolymers without Pasteurella haemolytica LPS
Etude des politiques relatives aux stratégies de gestion de la chimiorésistance dans le cadre de la lutte contre la trypanosomose en Afrique de l'Ouest: cas du Mali
Discussion sur l’etude des politiques relatives aux stratégies de gestion de la chimiorésistance dans le cadre de la lutte contre la trypanosomose en Afrique de l’Ouest, Mali. Le projet a pour objectif d’assurer l’efficacité des trypanocides comme une composante effective des strategies intégrées et améliorées de contrôle de Ia trypanosomose animale dans Ia region ouest-africaine. Pour atteindre cet objectif, des organisations nationales de recherche et de developpement, des institutions internationales et régionales de recherche, et des universités allemandes travaillent en partenariat afin de développer aux niveaux local et regional des strategies de reduction de risque de Ia chimiorésistance. L’accent est mis principalement sur l‘information et des supports techniques aux paysans, aux prestataires de service en sante animale, aux vétérinaires professionnels et aux décideurs politiques. Les informations et supports techniques ont pour but de promouvoir Ia lutte intégrée et l’utilisation rationnelle des trypanocides afin de réduire les risques a long terme de Ia chimiorésistance sans compromettre Ia capacité des éleveurs a pouvoir protéger leurs animaux contre les effets néfastes de la trypanosomose animale. Le projet est réalisé au Burkina Faso, au Mali et en Guinée par l’lnstitut International de Recherche sur l’Elevage (lLRl) en collaboration avec d’autres organisations. Des approaches de solutions sont alors proposees de maniere a apporter une solution durable au phenomene de la chimioresistance
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