Les Cahiers du GERAD ISSN : 0711 – 2440
نویسندگان
چکیده
Conjectures in graph theory have multiple forms and involve graph invariants, graph classes, subgraphs, minors and other concepts in premisses and/or conclusions. Various abstract criteria have been proposed in order to find interesting ones with computeraided or automated systems for conjecture-making. Beginning with the observation that famous theorems (and others) have first been conjectures, if only in the minds of those who obtained them, we review forms that they take. We also give examples of conjectures of such forms obtained with the help of, or by, computers when it is the case. It appears that many forms are unexplored and so computer-assisted and automated conjecture-making in graph theory, despite many successes, is pretty much at its beginning.
منابع مشابه
Les Cahiers du GERAD ISSN : 0711 – 2440
Let G = (V,E,w) be a graph with vertex and edge sets V and E, respectively, and w : E → IR a function which assigns a positive weigth or length to each edge of G. G is called a realization of a finite metric space (M,d), with M = {1, ..., n} if and only if {1, ..., n} ⊆ V and d(i, j) is equal to the length of the shortest chain linking i and j in G ∀i, j = 1, ..., n. A realization G of (M,d), i...
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