5,411 research outputs found
Lattic path proofs of extended Bressoud-Wei and Koike skew Schur function identities
Our recent paper provides extensions to two classical determinantal results of Bressoud and Wei, and of Koike. The proofs in that paper were algebraic. The present paper contains combinatorial lattice path proofs
Bad News for Chordal Partitions
Reed and Seymour [1998] asked whether every graph has a partition into
induced connected non-empty bipartite subgraphs such that the quotient graph is
chordal. If true, this would have significant ramifications for Hadwiger's
Conjecture. We prove that the answer is `no'. In fact, we show that the answer
is still `no' for several relaxations of the question
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