[PDF] Top 20 An injective version of the 1-2-3 Conjecture

... interpreting the 1-2-3 Conjecture. On the one hand, the conjecture states that for almost all graphs G, we should be able to “encode” a proper colouring via a ... Voir le document complet

... are the locally irregular ones, ...denotes the degree of the vertex x), those G with χ Σ (G) = 2 do not admit a “good” characterization, unless P=NP (as first proved by Dudek and Wajc ... Voir le document complet

... edges of G get weighted by w 0 ; this is in particular the case for the private edges not chosen in the last ...some of which, in particular the ones with no edges, must be ... Voir le document complet

... summary of some of these investigations is deferred to the next ...section. The current work is also related to locally irregular decompositions, which were considered as a de- compositional ... Voir le document complet

... Keywords: 1–2–3 Conjecture, locally irregular graph, graph decomposition ...graph of order at least 2 cannot be irregular, ...though. The least k so that an ... Voir le document complet

... edge-weightings, the goal is to make adjacent vertices distinguishable via their incident ...tinguish the adjacent vertices in a stronger ...least 2. An edge-weighting with this stronger ... Voir le document complet

... Table 1, we have listed all progress we are aware of regarding directed variants of the 1-2-3 Conjecture defined over the parameters σ − , σ + ...variant, ... Voir le document complet

... number of weights in a sum-colouring k-arc-weighting (if any) of D is denoted χ e Ł ...investigating the parameter χ e Ł , let us, reusing the notions and termi- nology above, describe ... Voir le document complet

... 1-2-3 Conjecture (product ...≤ 3. The multiset version of the 1-2-3 Conjecture was introduced by Addario-Berry, Aldred, Dalal and ... Voir le document complet

... on the collections of fields in 4.2 and 4.3. On one hand, the collection of extensions J~ of J~o with ~k - 1 mod i is cofinal, in that any extension of l~o is a subfield ... Voir le document complet

... + 2) and 0 < ε < 1 (where C ε is a constant independent from k and d), • (Cn) d+1 for any d and k ≥ d + 2 (where C is a constant independent from k and ...that the 7-recolouring ... Voir le document complet

... both the 1-2-3 Conjecture and the 1-2 Conjecture were considered in the more general list ...instead of weighting all the graph elements ... Voir le document complet

... plan of the paper is as follows: In section 2 we define the geometric objects, as for example Weierstrass models, discriminants and Weierstrass points, to state and discuss the results ... Voir le document complet

... On the field IK, the same question makes sens too and similarly, ...≥ 3, f n f 0 has no quasi-exceptional value different from 0 ...= 2 and n = 1, several particular solutions were ... Voir le document complet

... after the universality class of the IR fixed point, it is natural to wonder [17] whether the Hamiltonian might be substituted by an integrable version without affecting ... Voir le document complet

... ≥ 2, there is no absolute constant bounding χ r Σ (G) above for every r-nice graph G, a legitimate question is about the best way to express bounds on this parameter in ...From the two constructions ... Voir le document complet

... labelling of the remaining graph to a desired one of G, by labelling the edges of the C i ’s so that only a few 3’s are ...4.4 An upper bound for Halin graphs A ... Voir le document complet

... cycles of G. To define those cycles, let us consider the following ...− the cactus obtained from G by repeatedly deleting vertices of degree 1, until the remaining graph has ... Voir le document complet

... that the bound of Conjecture 1 might be ...in the article [9] containing his proof of the conjecture for very large ...In the conclusion of [9] ... Voir le document complet

... favour of the number of assigned 2’s, that is so huge that it cannot be caught up by the labelling freedom of G m and the copies of the corrector gadget ... Voir le document complet