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Given a positive integer n and a family F of graphs, let R * (n,F) denote the maximum number of colors in an edge-coloring of K n such that no subgraph of K n belonging to F has distinct colors on its edges. We determine R * (n,T k ), where T k is the family of trees with k edges. We derive general bounds for R * (n,T), where T is an arbitrary...
In 1957, Kotzig proved that the line graph of a snark (non edge-3-colorable cubic graph) is a 4-coloring-snark (non edge-4-colorable 4-regular graph). In this paper we present a reverse construction, i.e., we construct snarks from 4-coloring-snarks. In a similar way, we construct graphs without nowhere-zero 3-flows from snarks.
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