On {a,b}-edge-weightings of bipartite graphs with odd a,b
Résumé
For any $S⊂ℤ$ we say that a graph G has the S-property if there exists an S-edge-weighting $w:E(G)→S$ such that for any pair of adjacent vertices u,v we have $Σ_{e∈E(v)} w(e) ≠ Σ_{e∈E(u)} w(e)$, where E(v) and E(u) are the sets of edges incident to v and u respectively. This work focuses on {a,a+2}-edge-weightings where $a∈ℤ$ is odd. We show that a 2-connected bipartite graph has the {a,a+2}-property if and only if it is not a so-called odd multi-cactus. In the case of trees, we show that only one case is pathological. That is, we show that all trees have the {a,a+2}-property for odd $a≠−1$, while there is an easy characterization of trees without the {−1,1}-property.
Domaines
Mathématique discrète [cs.DM]
Origine : Fichiers produits par l'(les) auteur(s)
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