699 research outputs found
Asymmetric coloring games on incomparability graphs
Consider the following game on a graph : Alice and Bob take turns coloring
the vertices of properly from a fixed set of colors; Alice wins when the
entire graph has been colored, while Bob wins when some uncolored vertices have
been left. The game chromatic number of is the minimum number of colors
that allows Alice to win the game. The game Grundy number of is defined
similarly except that the players color the vertices according to the first-fit
rule and they only decide on the order in which it is applied. The -game
chromatic and Grundy numbers are defined likewise except that Alice colors
vertices and Bob colors vertices in each round. We study the behavior of
these parameters for incomparability graphs of posets with bounded width. We
conjecture a complete characterization of the pairs for which the
-game chromatic and Grundy numbers are bounded in terms of the width of
the poset; we prove that it gives a necessary condition and provide some
evidence for its sufficiency. We also show that the game chromatic number is
not bounded in terms of the Grundy number, which answers a question of Havet
and Zhu
On-line partitioning of width w posets into w^O(log log w) chains
An on-line chain partitioning algorithm receives the elements of a poset one
at a time, and when an element is received, irrevocably assigns it to one of
the chains. In this paper, we present an on-line algorithm that partitions
posets of width into chains. This improves over
previously best known algorithms using chains by Bosek and
Krawczyk and by Bosek, Kierstead, Krawczyk, Matecki, and Smith. Our algorithm
runs in time, where is the width and is the size of
a presented poset.Comment: 16 pages, 10 figure
Coloring triangle-free rectangle overlap graphs with colors
Recently, it was proved that triangle-free intersection graphs of line
segments in the plane can have chromatic number as large as . Essentially the same construction produces -chromatic
triangle-free intersection graphs of a variety of other geometric
shapes---those belonging to any class of compact arc-connected sets in
closed under horizontal scaling, vertical scaling, and
translation, except for axis-parallel rectangles. We show that this
construction is asymptotically optimal for intersection graphs of boundaries of
axis-parallel rectangles, which can be alternatively described as overlap
graphs of axis-parallel rectangles. That is, we prove that triangle-free
rectangle overlap graphs have chromatic number , improving on
the previous bound of . To this end, we exploit a relationship
between off-line coloring of rectangle overlap graphs and on-line coloring of
interval overlap graphs. Our coloring method decomposes the graph into a
bounded number of subgraphs with a tree-like structure that "encodes"
strategies of the adversary in the on-line coloring problem. Then, these
subgraphs are colored with colors using a combination of
techniques from on-line algorithms (first-fit) and data structure design
(heavy-light decomposition).Comment: Minor revisio
Defective 3-Paintability of Planar Graphs
A -defective -painting game on a graph is played by two players:
Lister and Painter. Initially, each vertex is uncolored and has tokens. In
each round, Lister marks a chosen set of uncolored vertices and removes one
token from each marked vertex. In response, Painter colors vertices in a subset
of which induce a subgraph of maximum degree at most . Lister
wins the game if at the end of some round there is an uncolored vertex that has
no more tokens left. Otherwise, all vertices eventually get colored and Painter
wins the game. We say that is -defective -paintable if Painter has a
winning strategy in this game. In this paper we show that every planar graph is
3-defective 3-paintable and give a construction of a planar graph that is not
2-defective 3-paintable.Comment: 21 pages, 11 figure
An easy subexponential bound for online chain partitioning
Bosek and Krawczyk exhibited an online algorithm for partitioning an online
poset of width into chains. We improve this to with a simpler and shorter proof by combining the work of Bosek &
Krawczyk with work of Kierstead & Smith on First-Fit chain partitioning of
ladder-free posets. We also provide examples illustrating the limits of our
approach.Comment: 23 pages, 11 figure
Role of gut microbiota in pathogenesis of selected chronic diseases
The human digestive system is colonized by a huge number of microorganisms, that are referred to collectively as the gut microbiota. The composition of intestinal microorganisms are shaped from an early life and undergoes constant changes depending on the influence of external factors, such as: type of delivery, feeding the young child, diet in subsequent years of life, pharmaceuticals use, stress, lifestyle or infections and previous inflammation within the digestive tract. Despite transient changes in microbiota composition, the intestinal ecosystem is constantly striving to maintain homeostasis, both qualitative and quantitative, which is fundamental to human health and human development. Microbes present in the intestines are responsible for sealing the intestinal barrier, mucin production, stimulation of the angiogenesis process, supporting digestive processes by fermentation and decomposition of undigested food residues, vitamin production or protection from pathogenic microorganisms. As shown by numerous studies carried out in recent years, intestinal dysbiosis plays a fundamental role in the development of many chronic diseases such as inflammatory bowel disease, diabetes, obesity, celiac disease, connective tissue diseases and others. Insightful understanding of the interactions between microorganisms and the host organisms can provide new information about pathogenesis of diseases as well as new ways to prevent and treat intestinal or systemic disorders. The aim of this work is to review the latest reports on the role of the gastrointestinal microbiome in selected chronic diseases
Krytyka kapitalizmu i liberalnej demokracji z perspektywy współczesnego buddyzmu. Wybrane przykłady tajskiej myśli społecznej
The article describes chosen concepts of Thai Buddhist thought, which is critical to liberal democracy and capitalist order. The examples of the thought are: Buddhadasa Bhikkhu's conception of "dhammic socialism"; the idea of "middle - way economics" forcing by Prayudh Payutto and Sulak Sivaraksa's thesis on balanced economics and moral governments. All three authors mentioned above refer to the doctrinal basis of the modern Theravada Buddhism mainstream in Thailand as well as they are recognized as the representatives of "Socially engaged Bhuddism".Artykuł omawia wybrane koncepcje tajskiej myśli buddyjskiej, krytycznej wobec liberalnej demokracji oraz kapitalistycznego porządku ekonomicznego. Przykładami tej myśli są: koncepcja "dhamicznego socjalizmu" Buddhadasy bhikkhu, założenia "ekonomii środka" Prayudha Payutto oraz tezy na temat zrównoważonej gospodarki i moralnych rządów Sulaka Sivaraksy. Wszyscy wymienieni autorzy bazują na doktrynalnych podstawach głównego nurtu współczesnego buddyzmu theravada w Tajlandii oraz są uznawani za reprezentantów "buddyzmu społecznie zaangażowanego"
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