Embedding trees in a hypercube is NP-complete
SIAM Journal on Computing
Discrete Mathematics
Combinatorics, Probability and Computing
A note on the Hopf-Stiefel function
European Journal of Combinatorics - Special issue on Eurocomb'03 - graphs and combinatorial structures
Optimal strong parity edge-coloring of complete graphs
Combinatorica
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A parity walk in an edge-coloring of a graph is a walk along which each color is used an even number of times. A parity edge-coloring (respectively, strong parity edge-coloring) is an edge-coloring in which there is no nontrivial parity path (respectively, open parity walk). The parity edge-chromatic number p(G) (respectively, strong parity edge-chromatic number $\widehat{p}(G)$ ) is the least number of colors in a parity edge-coloring (respectively, strong parity edge-coloring) of G. Notice that $\widehat{p}(G) \ge p(G) \ge \chi'(G) \ge \Delta(G)$ for any graph G. In this paper, we determine $\widehat{p}(G)$ and p(G) for some complete bipartite graphs and some products of graphs. For instance, we determine $\widehat{p}(K_{m,n})$ and p(K m,n ) for m驴n with n驴0,驴1,驴2 (mod 2驴lg驴m驴).