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Combinatorics, Complexity, and ChanceA Tribute to Dominic Welsh$
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Geoffrey Grimmett and Colin McDiarmid

Print publication date: 2007

Print ISBN-13: 9780198571278

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198571278.001.0001

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Combinatorics, Complexity, and Chance

László Lovász

Oxford University Press

This chapter introduces a matrix, the kth connection matrix, for a given graph parameter and integer k ≥ 0. The properties of these matrices are closely connected with properties of the parameter. For example, the rank of this matrix is considered the minimum number of real numbers that has to be communicated across a node-cut of size k in order to evaluate the invariant. It is shown that other properties of this matrix, like whether it is semidefinite, also turn out to have graph theoretic significance.

Keywords:   matrix, graph parameter, node connection matrices, edge-connection matrices, planar graphs

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