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)
Vanillin, a food additive, has been evaluated as a potential agent to treat sickle cell anemia. Earlier studies indicated that vanillin had moderate antisickling activity when compared with other aldehydes. We have determined by high performance liquid chromatography that vanillin reacts covalently with sickle hemoglobin (HbS) both in solution and in intact(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)