18 research outputs found
Homogeneous sets, clique-separators, critical graphs, and optimal -binding functions
Given a set of graphs, let be the optimal -binding function of
the class of -free graphs, that is,
In this paper, we combine the
two decomposition methods by homogeneous sets and clique-separators in order to
determine optimal -binding functions for subclasses of -free graphs
and of -free graphs. In particular, we prove the following
for each :
(i)
(ii) $\
f_{\{P_5,co-banner\}}^\star(\omega)=f^\star_{\{2K_2\}}(\omega)\in\mathcal{O}(\omega^2),\
f_{\{C_5,C_7,\ldots,banner\}}^\star(\omega)=f^\star_{\{C_5,3K_1\}}(\omega)\notin
\mathcal{O}(\omega),\ f_{\{P_5,C_4\}}^\star(\omega)=\lceil(5\omega-1)/4\rceil.G\chi(G)>\chi(G-u)u\in V(G)(P_5,banner)$-free graphs
A characterization of trees with equal 2-domination and 2-independence numbers
A set of vertices in a graph is a -dominating set if every vertex
of not in is adjacent to at least two vertices in , and is a
-independent set if every vertex in is adjacent to at most one vertex of
. The -domination number is the minimum cardinality of a
-dominating set in , and the -independence number is the
maximum cardinality of a -independent set in . Chellali and Meddah [{\it
Trees with equal -domination and -independence numbers,} Discussiones
Mathematicae Graph Theory 32 (2012), 263--270] provided a constructive
characterization of trees with equal -domination and -independence
numbers. Their characterization is in terms of global properties of a tree, and
involves properties of minimum -dominating and maximum -independent sets
in the tree at each stage of the construction. We provide a constructive
characterization that relies only on local properties of the tree at each stage
of the construction.Comment: 17 pages, 4 figure
Spanning trees of smallest maximum degree in subdivisions of graphs
\newcommand{\subdG}[1][G]{#1^\star}
Given a graph and a positive integer , we study the question whether
has a spanning tree of maximum degree at most where is
the graph that is obtained from by subdividing every edge once. Using
matroid intersection, we obtain a polynomial algorithm for this problem and a
characterization of its positive instances. We use this characterization to
show that has a spanning tree of bounded maximum degree if is
contained in some particular graph class. We study the class of 3-connected
graphs which are embeddable in a fixed surface and the class of
-connected -minor-free graphs for a fixed integer . We also give
tightness examples for most of these classes
Extending the MAX Algorithm for Maximum Independent Set
The maximum independent set problem is an NP-hard problem. In this paper, we consider Algorithm MAX, which is a polynomial time algorithm for finding a maximal independent set in a graph G. We present a set of forbidden induced subgraphs such that Algorithm MAX always results in finding a maximum independent set of G. We also describe two modifications of Algorithm MAX and sets of forbidden induced subgraphs for the new algorithms
On Sequential Heuristic Methods for the Maximum Independent Set Problem
We consider sequential heuristics methods for the Maximum Independent Set (MIS) problem. Three classical algorithms, VO [11], MIN [12], or MAX [6] , are revisited. We combine Algorithm MIN with the α-redundant vertex technique[3]. Induced forbidden subgraph sets, under which the algorithms give maximum independent sets, are described. The Caro-Wei bound [4,14] is verified and performance of the algorithms on some special graphs is considered
Evidence against a major role of adenosine in oxygen-dependent regulation of erythropoietin in rats
Evidence against a major role of adenosine in oxygen-dependent regulation of erythropoietin in rats. This in vivo study investigated whether adenosine (ADO) plays a role in oxygen-dependent production of erythropoietin (EPO). Exposure of rats to 0.075% carbon monoxide (CO) for four hours was used as a stimulus for EPO production. To inhibit potential effects of ADO, rats were treated with the non-specific ADO antagonist theophylline, the selective ADO A1 receptor blockers DPCPX and KW-3902, the selective ADO A2 receptor blocker DMPX, and AOPCP, an inhibitor of 5′-ectonucleotidase, an ADO generating enzyme that is expressed on the surface of EPO producing cells. To stimulate ADO receptor activity, animals were treated with the selective ADO A1 and A2 receptor agonists CHA and CGS 21680, the ADO reuptake inhibitors dipyridamole and soluflazine and the ADO desaminase inhibitor EHNA. At doses known to interfere with ADO signal transmission in vivo, none of these substances either influenced EPO serum levels in normoxic rats or affected the approximately 30-fold rise in EPO serum levels and the increase in renal EPO mRNA after exposure to carbon monoxide. Continuous administration of theophylline to normoxic rats for seven days did not alter hematocrit, hemoglobin or EPO serum levels. Taken together, these experiments do not support the hypothesis that ADO plays an important role in the regulation of EPO production
Acyclic, star and injective colouring: bounding the diameter
We examine the effect of bounding the diameter for wellstudied variants of the Colouring problem. A colouring is acyclic, star, or injective if any two colour classes induce a forest, star forest or disjoint union of vertices and edges, respectively. The corresponding decision problems are Acyclic Colouring, Star Colouring and Injective Colouring. The last problem is also known as L(1, 1)-Labelling and we also consider the framework of L(a, b)-Labelling. We prove a number of (almost-)complete complexity classifications, in particular, for Acyclic 3-Colouring, Star 3-Colouring and L(1, 2)-Labellin