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- W2297478040 abstract "Let $$C subseteq [r]^m$$C⊆[r]m be a code such that any two words of C have Hamming distance at least t. It is not difficult to see that determining a code C with the maximum number of words is equivalent to finding the largest n such that there is an r-edge-coloring of $$K_{m, n}$$Km,n with the property that any pair of vertices in the class of size n has at least t alternating paths (with adjacent edges having different colors) of length 2. In this paper we consider a more general problem from a slightly different direction. We are interested in finding maximum t such that there is an r-edge-coloring of $$K_{m,n}$$Km,n such that any pair of vertices in class of size n is connected by t internally disjoint and alternating paths of length 2k. We also study a related problem in which we drop the assumption that paths are internally disjoint. Finally, we introduce a new concept, which we call alternating connectivity. Our proofs make use of random colorings combined with some integer programs." @default.
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- W2297478040 date "2017-02-06" @default.
- W2297478040 modified "2023-09-24" @default.
- W2297478040 title "On the Number of Alternating Paths in Bipartite Complete Graphs" @default.
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- W2297478040 doi "https://doi.org/10.1007/s00373-017-1771-x" @default.
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