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We study the multicolor Ramsey numbers for paths and even cycles, Rk(Pn) and Rk(Cn), which are the smallest integers N such that every coloring of the complete graph KN has a monochromatic copy of Pn or Cn respectively. For a long time, Rk(Pn) has only been known to lie between (k−1+o(1))n and (k+o(1))n. A recent breakthrough by Sárközy and later improvement by Davies, Jenssen and Roberts give an upper bound of (k−14+o(1))n. We improve the upper bound to (k−12+o(1))n. Our approach uses structural insights in connected graphs without a large matching. Show more
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Journal / seriesThe Electronic Journal of Combinatorics
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PublisherElectronic Journal of Combinatorics
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