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Every minor-closed class of matroids of bounded branch-width can be characterized by a minimal list of excluded minors, but unlike graphs, this list could be infinite in general. However, for each fixed finite field
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Seminars and Colloquiums
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This talk follows on from the recent talk of Pascal Gollin in this seminar series, but will aim to be accessible for newcomers. Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. By … |
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We examine algorithmic extensions of two classic results of extremal combinatorics. First, the theorem of Dirac from 1952 asserts that a 2-connected graph G with the minimum vertex degree d>1, is either Hamiltonian or contains a cycle of length at least 2d. Second, the theorem of Erdős-Gallai from 1959, states that a 2-connected graph G … |
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It is known that the rank- and tree-width of the random graph |
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The Ramsey number |
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Suppose that |
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In 1982 Galvin, Rival, and Sands proved that in |
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