https://nova.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:37349 Wed 14 Oct 2020 14:22:17 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:37764 0⊆S₁⊆S₂⊆⋯ be defined as follows: S₁ is obtained from S₀ by adding all out-neighbors of vertices in S₀. For k⩾2, S_k is obtained from S_k−1 by adding all vertices w such that for some vertex v∈S_k−1, w is the unique out-neighbor of v in V∖S_k−1. We set M(S)=S₀∪S₁∪⋯, and call S a power dominating set for G if M(S)=V(G). The minimum cardinality of such a set is called the power domination number of G. In this paper, we determine the power domination numbers of de Bruijn and Kautz digraphs.]]> Wed 14 Apr 2021 12:21:11 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:30480 G = (V,E) admits an H-covering if every edge in E is contained in a subgraph H’= (V’, E’) of G which is isomorphic to H. In this case we say that G is H-supermagic if there is a bijection f : V ⋃ E → {1,...,|V| + |E|} such that f(V) = {1,...,|V|} and ∑_vϵV(H')f(v)+∑_vϵV(H')f(e) is constant over all subgraphs H' of G which are isomorphic to H. Extending results from [M. Roswitha and E.T. Baskoro, Amer. Inst. Physics Conf. Proc. 1450 (2012), 135-138], we show that the firecracker F_k,n is F_2,n-supermagic, the banana tree B_k,n is B_k-1,n-supermagic and the flower F_n is C₃-supermagic.]]> Wed 11 Apr 2018 14:06:23 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:32246 Wed 04 Sep 2019 12:18:04 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:32245 Wed 04 Sep 2019 12:18:03 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:19022 Wed 04 Sep 2019 11:13:46 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:17509 Wed 04 Sep 2019 11:04:58 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:26872 Wed 04 Sep 2019 10:37:58 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:29262 Wed 04 Sep 2019 10:12:13 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:33940 Wed 04 Sep 2019 10:04:28 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:33276 Wed 04 Sep 2019 09:55:27 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:31033 G=(V,E) and a set E₀⊂E, the incremental network design problem with minimum spanning trees asks for a sequence of edges e′₁,…,e′_T∈E∖E₀ minimizing [formula could not be replicated] where w(Xt) is the weight of a minimum spanning tree X_t for the subgraph (V,E₀∪{e′₁,…,e′_t}) and T=|E∖E₀|. We prove that this problem can be solved by a greedy algorithm.]]> Wed 04 Sep 2019 09:39:31 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:35653 Wed 02 Oct 2019 10:01:58 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:52926 Wed 01 Nov 2023 09:36:11 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:35971 Wed 01 Jul 2020 11:14:42 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:32580 n → ℝ can be approximated by its McCormick relaxation. In particular, we are interested in the smallest number c such that the difference between the concave upper bounding and convex lower bounding functions obtained from the McCormick relaxation approach is at most c times the difference between the concave and convex envelopes. Answering a question of Luedtke, Namazifar and Linderoth, we show that this factor c cannot be bounded by a constant independent of n. More precisely, we show that for a random bilinear function b we have asymptotically almost surely c ⩾ √n/4. On the other hand, we prove that c ⩽ 600√n, which improves the linear upper bound proved by Luedtke, Namazifar and Linderoth. In addition, we present an alternative proof for a result of Misener, Smadbeck and Floudas characterizing functions b for which the McCormick relaxation is equal to the convex hull.]]> Tue 03 Sep 2019 18:27:33 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:32583 Tue 03 Sep 2019 18:23:44 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:34786 zero forcing set if by iterating this process, all of the vertices in G become black. The zero forcing number of G is the minimum cardinality of a zero forcing set in G, and is denoted by Z(G). Davila and Kenter have conjectured in 2015 that Z(G)≥(g-3)(δ-2)+ δ where g and δ denote the girth and the minimum degree of G, respectively. This conjecture has been proven for graphs with girth g≤10. In this note, we present a proof for g≥5, d≥2, thereby settling the conjecture.]]> Tue 01 Sep 2020 11:52:36 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:24113 [n]\A there is an A ∈ A with X ⊆ A or A ⊆ X, and (3) A is r-regular, i.e., every point x ∈ [n] is contained in exactly r members of A. We prove lower bounds on r, and we describe constructions for regular maximal antichains with small regularity.]]> Thu 30 May 2019 19:13:22 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:40962 Thu 21 Jul 2022 08:31:15 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:37218 Thu 15 Apr 2021 12:01:59 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13719 Sat 24 Mar 2018 08:22:59 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13720 Sat 24 Mar 2018 08:22:59 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:20238 Sat 24 Mar 2018 08:05:41 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:19239 Sat 24 Mar 2018 07:54:56 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:25381 Sat 24 Mar 2018 07:39:09 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:27959 Sat 24 Mar 2018 07:38:44 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:23745 unique winner UCM problem and the co-winner UCM problem and argue that they have substantially different necessary and sufficient conditions for the existence of a successful manipulation.]]> Sat 24 Mar 2018 07:16:57 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:24379 conditional non-anticipativity constraints form a very large class, with cardinality in the order of the square of the number of scenarios. However, depending on the properties of the set of scenarios considered, only very few of these constraints may be required for validity of the model. Here we characterize minimal sufficient sets of non-anticipativity constraints, and prove that their matroid structure enables sets of minimum cardinality to be found efficiently, under general conditions on the structure of the scenario set.]]> Sat 24 Mar 2018 07:16:17 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:23473 Sat 24 Mar 2018 07:13:00 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:25179 Mon 24 Jun 2019 18:45:04 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:27960 Mon 23 Sep 2019 11:29:20 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:37591 f on the n-dimensional unit cube [0, 1] ⁿ. Extended formulations for this convex hull are obtained by taking subsets of the facets of the Boolean Quadric Polytope (BQP). Extending existing results, we propose a systematic study of properties of f that guarantee that certain classes of BQP facets are sufficient for an extended formulation. We use a modification of Zuckerberg’s geometric method for proving convex hull characterizations (Zuckerberg, 2016) to prove some initial results in this direction. In particular, we provide small-sized extended formulations for bilinear functions whose corresponding graph is either a cycle with arbitrary edge weights or a clique or an almost clique with unit edge weights.]]> Mon 22 Feb 2021 13:44:52 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:46210 Mon 15 Apr 2024 11:13:59 AEST ]]>