53 research outputs found
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Combinatorics
Combinatorics is a fundamental mathematical discipline which focuses on the study of discrete objects and their properties. The current workshop brought together researchers from diverse fields such as Extremal and Probabilistic Combinatorics, Discrete Geometry, Graph theory, Combiantorial Optimization and Algebraic Combinatorics for a fruitful interaction. New results, methods and developments and future challenges were discussed. This is a report on the meeting containing abstracts of the presentations and a summary of the problem session
Basic Neutrosophic Algebraic Structures and their Application to Fuzzy and Neutrosophic Models
The involvement of uncertainty of varying degrees when the total of the
membership degree exceeds one or less than one, then the newer mathematical
paradigm shift, Fuzzy Theory proves appropriate. For the past two or more
decades, Fuzzy Theory has become the potent tool to study and analyze
uncertainty involved in all problems. But, many real-world problems also abound
with the concept of indeterminacy. In this book, the new, powerful tool of
neutrosophy that deals with indeterminacy is utilized. Innovative neutrosophic
models are described. The theory of neutrosophic graphs is introduced and
applied to fuzzy and neutrosophic models. This book is organized into four
chapters. In Chapter One we introduce some of the basic neutrosophic algebraic
structures essential for the further development of the other chapters. Chapter
Two recalls basic graph theory definitions and results which has interested us
and for which we give the neutrosophic analogues. In this chapter we give the
application of graphs in fuzzy models. An entire section is devoted for this
purpose. Chapter Three introduces many new neutrosophic concepts in graphs and
applies it to the case of neutrosophic cognitive maps and neutrosophic
relational maps. The last section of this chapter clearly illustrates how the
neutrosophic graphs are utilized in the neutrosophic models. The final chapter
gives some problems about neutrosophic graphs which will make one understand
this new subject.Comment: 149 pages, 130 figure
A survey of parameterized algorithms and the complexity of edge modification
The survey is a comprehensive overview of the developing area of parameterized algorithms for graph modification problems. It describes state of the art in kernelization, subexponential algorithms, and parameterized complexity of graph modification. The main focus is on edge modification problems, where the task is to change some adjacencies in a graph to satisfy some required properties. To facilitate further research, we list many open problems in the area.publishedVersio
An extensive English language bibliography on graph theory and its applications
Bibliography on graph theory and its application
Hamilton decompositions of regular expanders: a proof of Kelly's conjecture for large tournaments
A long-standing conjecture of Kelly states that every regular tournament on n
vertices can be decomposed into (n-1)/2 edge-disjoint Hamilton cycles. We prove
this conjecture for large n. In fact, we prove a far more general result, based
on our recent concept of robust expansion and a new method for decomposing
graphs. We show that every sufficiently large regular digraph G on n vertices
whose degree is linear in n and which is a robust outexpander has a
decomposition into edge-disjoint Hamilton cycles. This enables us to obtain
numerous further results, e.g. as a special case we confirm a conjecture of
Erdos on packing Hamilton cycles in random tournaments. As corollaries to the
main result, we also obtain several results on packing Hamilton cycles in
undirected graphs, giving e.g. the best known result on a conjecture of
Nash-Williams. We also apply our result to solve a problem on the domination
ratio of the Asymmetric Travelling Salesman problem, which was raised e.g. by
Glover and Punnen as well as Alon, Gutin and Krivelevich.Comment: new version includes a standalone version of the `robust
decomposition lemma' for application in subsequent paper
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