Robin Thomas

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A graph is a minor of another if the first can be obtained from a sub-graph of the second by contracting edges. An excluded minor theorem describes the structure of graphs with no minor isomorphic to a prescribed set of graphs. Splitter theorems are tools for proving excluded minor theorems. We discuss splitter theorems for internally 4-connected graphs and(More)
For each infinite cardinal k we give several necessary and sufficient conditions for a graph not to contain a minor isomorphic to the infinite k-branching tree in terms of a certain kind of a "tree-decomposition," in terms of a "path-decomposition," and also in terms of a "cops-and-robber game." We also give necessary and sufficient conditions for a graph(More)
A hypergraph H has tree-width k (a notion introduced by Robertson and Seymour) if k is the least integer such that H admits a tree-decomposition of tree-width k. We prove a compactness theorem for this notion, that is, if every finite subhypergraph of H has tree-width < k, then H itself has tree-width < k. This result will be used in a later paper on(More)
Granulopoiesis-related genes are distinctively upregulated in peripheral leukocytes of patients with antineutrophil cytoplasmic autoantibodies (ANCA)-associated glomerulonephritis. Affymetrix microarrays identified the upregulation of nine neutrophilic primary granule genes, including myeloperoxidase (MPO) and proteinase 3 (PR3), plus five secondary granule(More)