On the Factorization of Graphs with Exactly One Vertex of Infinite Degree

AbstractWe give a necessary and sufficient condition for the existence of a 1-factor in graphs with exactly one vertex of infinite degree

Dominating the Erdos-Moser theorem in reverse mathematics

The Erdos-Moser theorem (EM) states that every infinite tournament has an infinite transitive subtournament. This principle plays an important role in the understanding of the computational strength of Ramsey's theorem for pairs (RT^2_2) by providing an alternate proof of RT^2_2 in terms of EM and the ascending descending sequence principle (ADS). In this paper, we study the computational weakness of EM and construct a standard model (omega-model) of simultaneously EM, weak K\"onig's lemma and the cohesiveness principle, which is not a model of the atomic model theorem. This separation answers a question of Hirschfeldt, Shore and Slaman, and shows that the weakness of the Erdos-Moser theorem goes beyond the separation of EM from ADS proven by Lerman, Solomon and Towsner.Comment: 36 page

Concepts of Optimality and Their Uses

Lecture to the memory of Alfred Nobel, December 11, 1975allocation of resources;

Graph classes and forbidden patterns on three vertices

This paper deals with graph classes characterization and recognition. A popular way to characterize a graph class is to list a minimal set of forbidden induced subgraphs. Unfortunately this strategy usually does not lead to an efficient recognition algorithm. On the other hand, many graph classes can be efficiently recognized by techniques based on some interesting orderings of the nodes, such as the ones given by traversals. We study specifically graph classes that have an ordering avoiding some ordered structures. More precisely, we consider what we call patterns on three nodes, and the recognition complexity of the associated classes. In this domain, there are two key previous works. Damashke started the study of the classes defined by forbidden patterns, a set that contains interval, chordal and bipartite graphs among others. On the algorithmic side, Hell, Mohar and Rafiey proved that any class defined by a set of forbidden patterns can be recognized in polynomial time. We improve on these two works, by characterizing systematically all the classes defined sets of forbidden patterns (on three nodes), and proving that among the 23 different classes (up to complementation) that we find, 21 can actually be recognized in linear time. Beyond this result, we consider that this type of characterization is very useful, leads to a rich structure of classes, and generates a lot of open questions worth investigating.Comment: Third version version. 38 page

Extremal results in sparse pseudorandom graphs

Szemer\'edi's regularity lemma is a fundamental tool in extremal combinatorics. However, the original version is only helpful in studying dense graphs. In the 1990s, Kohayakawa and R\"odl proved an analogue of Szemer\'edi's regularity lemma for sparse graphs as part of a general program toward extending extremal results to sparse graphs. Many of the key applications of Szemer\'edi's regularity lemma use an associated counting lemma. In order to prove extensions of these results which also apply to sparse graphs, it remained a well-known open problem to prove a counting lemma in sparse graphs. The main advance of this paper lies in a new counting lemma, proved following the functional approach of Gowers, which complements the sparse regularity lemma of Kohayakawa and R\"odl, allowing us to count small graphs in regular subgraphs of a sufficiently pseudorandom graph. We use this to prove sparse extensions of several well-known combinatorial theorems, including the removal lemmas for graphs and groups, the Erd\H{o}s-Stone-Simonovits theorem and Ramsey's theorem. These results extend and improve upon a substantial body of previous work.Comment: 70 pages, accepted for publication in Adv. Mat

Evaluation of older people\u27s knowledge, awareness, motivation and perceptions about falls and falls prevention in residential aged care homes: A tale of two cities

Falls prevention strategies can only be effective in reducing falls amongst older people if they are adopted and enacted in their daily lives. There is limited evidence identifying what older people in residential aged care (RAC) homes understand about falls and falls prevention, or what may limit or enable their adoption of strategies. This study was conducted in two countries and explored older people’s knowledge and awareness of falls and their preferences, opportunities and motivation to undertake falls prevention strategies. A cross-sectional survey was administered to participants (N = 70) aged 65 years and over, living in six RAC homes in Perth, Australia and six RAC homes in Swansea, Wales, United Kingdom. Participants had limited knowledge about intrinsic falls risk factors and strategies to address these and frequently expressed self-blame regarding falling. Almost all (N = 67, 95.7%) participants felt highly motivated to maintain their current functional mobility and independence in everyday tasks. Key preferences for receiving falls prevention messages favoured a positive approach promoting wellness and independence (N = 41, 58.6%) via pictorial posters or brochures (N = 37, 52.9%) and small group discussions preferably with demonstrations (N = 18, 25.7%). Findings from this study may assist organisations and staff to more effectively engage with older people living in RAC about falls prevention and design targeted resources to address the motivations and preferences of this population

THE ELECTRONIC JOURNAL OF COMBINATORICS (2014), DS1.14 References

and Computing 11. The results of 143 references depend on computer algorithms. The references are ordered alphabetically by the last name of the first author, and where multiple papers have the same first author they are ordered by the last name of the second author, etc. We preferred that all work by the same author be in consecutive positions. Unfortunately, this causes that some of the abbreviations are not in alphabetical order. For example, [BaRT] is earlier on the list than [BaLS]. We also wish to explain a possible confusion with respect to the order of parts and spelling of Chinese names. We put them without any abbreviations, often with the last name written first as is customary in original. Sometimes this is different from the citations in other sources. One can obtain all variations of writing any specific name by consulting the authors database of Mathematical Reviews a

Summer High School Apprenticeship Research Program (SHARP) of the National Aeronautics and Space Administration

A total of 125 talented high school students had the opportunity to gain first hand experience about science and engineering careers by working directly with a NASA scientist or engineer during the summer. This marked the fifth year of operation for NASA's Summer High School Apprenticehsip Research Program (SHARP). Ferguson Bryan served as the SHARP contractor and worked closely with NASA staff at Headquarters and the eight participating sites to plan, implement, and evaluate the Program. The main objectives were to strengthen SHARP and expand the number of students in the Program. These eight sites participated in the Program: Ames Research Center North, Ames' Dryden Flight Research Facility, Goddard Space Flight Center, Goddard's Wallops Flight Facility, Kennedy Space Center, Langley Research Center, Lewis Research Center, and Marshall Space Flight Center