Being Coloured and Looking Coloured

Coloured Spectacles

Properly Coloured Hamiltonian Paths in Edge-coloured Complete Graphs

We consider edge-coloured complete graphs. A path or cycle Q is called properly coloured (PC) if any two adjacent edges of Q differ in colour. Our note is inspired by the following conjecture by B. Bollobás and P. Erdős (1976) : if G is an edge-coloured complete graph on n vertices in which the maximum monochromatic degree of every vertex is less than bn/2c, then G contains a PC Hamiltonian cyc...

Large 2-Coloured Matchings in 3-Coloured Complete Hypergraphs

We prove the generalized Ramsey-type result on large 2-coloured matchings in a 3-coloured complete 3-uniform hypergraph, supporting a conjecture by A. Gyárfás.

Multi-Coloured Hamilton Cycles In Random Edge-Coloured Graphs

We de ne a space of random edge-coloured graphs Gn;m; which correspond naturally to edge -colourings of Gn;m. We show that there exist constants K0; K1 21 such that provided m K0n logn and K1n then a random edge coloured graph contains a multi-coloured Hamilton cycle with probability tending to 1, as the number of vertices n tends to in nity.

Are 'Scientific' Objects Coloured?

'In a world of "scientific" objects, objects characterizable by the vocabulary of physics alone, in a world governed by what we now believe to be the laws of nature, can anything be coloured?' I am here concerned to examine the claims of those physicalists who are disposed to give an affirmative answer to that question. In so doing, I shall restrict my attention to the physics of the present ti...