24 th Coast Combinatorics Conference and 4 th BC Combinatorics Day
نویسندگان
چکیده
Richard C. Brewster, Thompson Rivers University A Dichotomy Theorem for Circular Colouring Reconfiguration The “reconfiguration problem” for circular colourings asks, given two (p, q)colourings f and g of a graph G, is it possible to transform f into g by changing the colour of one vertex at a time such that every intermediate mapping is a (p, q)-colouring? We show that this problem can be solved in polynomial time for 2 ≤ p/q < 4 and is PSPACE-complete for p/q ≥ 4. This generalizes a known dichotomy theorem for reconfiguring classical graph colourings. Joint with Sean McGuinness (Thompson Rivers University), Ben Moore (Simon Fraser University) and Jon Noel (Oxford University). Justin Chan, Simon Fraser University Suitable cores and arrays An array with N rows and v columns where every row is a permutation of 1 to v is a (N, v, t)-suitable core if each symbol precedes each subset of s others in at least t−s rows for all 0 ≤ s ≤ t−1. If the statement applies only for s = t− 1, then the array is a (N, v, t)-suitable array. Dushnik and Spencer first studied suitable arrays, looking for arrays with minimum N given v and t. Colbourn linked the two types of arrays and constructed two infinite families of suitable cores, presenting results on the largest possible v given N and t. We give examples of suitable cores for new parameter triples (N, v, t), and nonexistence results whose proof uses elementary combinatorial arguments as well as Ramsey theory.
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تاریخ انتشار 2016