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EIGENVALUES OF GRAPHS
ON THE AXIOMATIC FOUNDATIONS
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4-colouring 4-colourings of Q adjacent appear apply assume Axiom blue bounded called chromials cluster cocircuit common complete condition Conjecture connected graph consider consisting construction contains corresponding defined definition denote digraph directed distinct dual edges edges of G eigenvalues elements equivalent example EXERCISE exists faces fact Figure finite follows Four Colour give given graph G graphoid green Hamiltonian circuit Hence included interchange interesting joined Kempe chains known least Lemma less linear lines Math matrix matroid means method minimal networks obtained ordering pair path planar graph plane points polyhedral graph polynomial polytopes possible pre-graphoid present problem proof prove question reader reducibility references regular respect satisfies sequence shown simple subgraph subsets Suppose symmetric symmetric matrix Theorem theory tree triangulation true U-extension valency values vector vertex vertices write