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Dans cet article, nous essayons de faire le point sur les résultats concernant les aspects combinatoires et algorithmiques des ordres médians et des ordres de Slater des tournois. La plupart des résultats recensés sont tirés de différentes publications ; plusieurs sont originaux.
The orientation distance graph 𝓓ₒ(G) of a graph G is defined as the graph whose vertex set is the pair-wise non-isomorphic orientations of G, and two orientations are adjacent iff the reversal of one edge in one orientation produces the other. Orientation distance graphs was introduced by Chartrand et al. in 2001. We provide new results about orientation distance graphs and simpler proofs to existing results, especially with regards to the bipartiteness of orientation distance graphs and the representation...
We provide the list of all paths with at most arcs with the property that if a graph admits an orientation such that one of the paths in our list admits no homomorphism to , then is -colourable.
We obtain some improved upper and lower bounds on the oriented chromatic number for different classes of products of graphs.
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