A generalization of Ramsey theory for graphs, with stars and complete graphs as forbidden subgraphs /

Includes bibliographical references.

A generalization of Ramsey theory for graphs /

Bibliography: p. 16.

A generalization of Ramsey theory for graphs /

Includes bibliographical references.

Diagonal forms, linear algebraic methods and Ramsey-type problems

This thesis focuses mainly on linear algebraic aspects of combinatorics. Let N_t(H) be an incidence matrix with edges versus all subhypergraphs of a complete hypergraph that are isomorphic to H. Richard M. Wilson and the author find the general formula for the Smith normal form or diagonal form of N_t(H) for all simple graphs H and for a very general class of t-uniform hypergraphs H.

As a continuation, the author determines the formula for diagonal forms of integer matrices obtained from other combinatorial structures, including incidence matrices for subgraphs of a complete bipartite graph and inclusion matrices for multisets.

One major application of diagonal forms is in zero-sum Ramsey theory. For instance, Caro's results in zero-sum Ramsey numbers for graphs and Caro and Yuster's results in zero-sum bipartite Ramsey numbers can be reproduced. These results are further generalized to t-uniform hypergraphs. Other applications include signed bipartite graph designs.

Research results on some other problems are also included in this thesis, such as a Ramsey-type problem on equipartitions, Hartman's conjecture on large sets of designs and a matroid theory problem proposed by Welsh.

Generalized Ramsey numbers for stars /

"UIUCDCS-R-81-1050"--Cover.

Properly coloured copies and rainbow copies of large graphs with small maximum degree

Let G be a graph on n vertices with maximum degree ?. We use the Lovasz local lemma to show the following two results about colourings ? of the edges of the complete graph Kn. If for each vertex v of Kn the colouring ? assigns each colour to at most (n - 2)/(22.4?2) edges emanating from v, then there is a copy of G in Kn which is properly edge-coloured by ?. This improves on a result of Alon, Jiang, Miller, and Pritikin [Random Struct. Algorithms 23(4), 409433, 2003]. On the other hand, if ? assigns each colour to at most n/(51?2) edges of Kn, then there is a copy of G in Kn such that each edge of G receives a different colour from ?. This proves a conjecture of Frieze and Krivelevich [Electron. J. Comb. 15(1), R59, 2008]. Our proofs rely on a framework developed by Lu and Szekely [Electron. J. Comb. 14(1), R63, 2007] for applying the local lemma to random injections. In order to improve the constants in our results we use a version of the local lemma due to Bissacot, Fernandez, Procacci, and Scoppola [preprint, arXiv:0910.1824]. (c) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 425436, 2012

The 3-colored Ramsey number of even cycles

Denote by R(L, L, L) the minimum integer N such that any 3-coloring of the edges of the complete graph on N vertices contains a monochromatic copy of a graph L. Bondy and Erdos conjectured that when L is the cycle C(n) on n vertices, R(C(n), C(n), C(n)) = 4n - 3 for every odd n > 3. Luczak proved that if n is odd, then R(C(n), C(n), C(n)) = 4n + o(n), as n -> infinity, and Kohayakawa, Simonovits and Skokan confirmed the Bondy-Erdos conjecture for all sufficiently large values of n. Figaj and Luczak determined an asymptotic result for the `complementary` case where the cycles are even: they showed that for even n, we have R(C(n), C(n), C(n)) = 2n + o(n), as n -> infinity. In this paper, we prove that there exists n I such that for every even n >= n(1), R(C(n), C(n), C(n)) = 2n. (C) 2009 Elsevier Inc. All rights reserved.

The Tripartite Ramsey Number for Trees

We prove that for all epsilon>0 there are alpha>0 and n(0)is an element of N such that for all n >= n(0) the following holds. For any two-coloring of the edges of Kn, n, n one color contains copies of all trees T of order t <=(3 - epsilon)n/2 and with maximum degree Delta(T)<= n(alpha). This confirms a conjecture of Schelp. (c) 2011 Wiley Periodicals, Inc. J Graph Theory 69: 264300, 2012

El Test de Ramsey y las lógicas condicionales

Frank Ramsey (1931) estableció ciertas condiciones que deberían cumplirse a fin de evaluar las proposiciones condicionales, conocidas hoy como Test de Ramsey (TR) En este trabajo se muestra que las teorías sobre condicionales contrafácticos de Chisholmj, Stalnaker y D. Lewis, satisfacen el TR y la incompatibilidad de TR con la Teoría de la revisión de creencias (AGM). En la última sección se analiza el comportamiento del TR en la propuesta de G. Grocco y L. Fariñas del Cerro, basada en una generalización del cálculo de Secuentes pero introduciendo la novedad de secuencias auxiliares cuya noción de consecuencia es no-monótona.

El Test de Ramsey y las lógicas condicionales

Frank Ramsey (1931) estableció ciertas condiciones que deberían cumplirse a fin de evaluar las proposiciones condicionales, conocidas hoy como Test de Ramsey (TR) En este trabajo se muestra que las teorías sobre condicionales contrafácticos de Chisholmj, Stalnaker y D. Lewis, satisfacen el TR y la incompatibilidad de TR con la Teoría de la revisión de creencias (AGM). En la última sección se analiza el comportamiento del TR en la propuesta de G. Grocco y L. Fariñas del Cerro, basada en una generalización del cálculo de Secuentes pero introduciendo la novedad de secuencias auxiliares cuya noción de consecuencia es no-monótona.

El Test de Ramsey y las lógicas condicionales

Frank Ramsey (1931) estableció ciertas condiciones que deberían cumplirse a fin de evaluar las proposiciones condicionales, conocidas hoy como Test de Ramsey (TR) En este trabajo se muestra que las teorías sobre condicionales contrafácticos de Chisholmj, Stalnaker y D. Lewis, satisfacen el TR y la incompatibilidad de TR con la Teoría de la revisión de creencias (AGM). En la última sección se analiza el comportamiento del TR en la propuesta de G. Grocco y L. Fariñas del Cerro, basada en una generalización del cálculo de Secuentes pero introduciendo la novedad de secuencias auxiliares cuya noción de consecuencia es no-monótona.

Feminist Disability Theory: Domestic Violence Against Women with a Disability

Women with a disability continue to experience social oppression and domestic violence as a consequence of gender and disability dimensions. Current explanations of domestic violence and disability inadequately explain several features that lead women who have a disability to experience violent situations. This article incorporates both disability and material feminist theory as an alternative explanation to the dominant approaches (psychological and sociological traditions) of conceptualising domestic violence. This paper is informed by a study which was concerned with examining the nature and perceptions of violence against women with a physical impairment. The emerging analytical framework integrating material feminist interpretations and disability theory provided a basis for exploring gender and disability dimensions. Insight was also provided by the women who identified as having a disability in the study and who explained domestic violence in terms of a gendered and disabling experience. The article argues that material feminist interpretations and disability theory, with their emphasis on gender relations, disablism and poverty, should be used as an alternative tool for exploring the nature and consequences of violence against women with a disability.