** Hamiltonian cycles in graphs were first studied in the 1850s. Since then, an impressive amount of research has been dedicated to identifying classes of graphs that allow Hamiltonian cycles, and to related questions. The corresponding decision problem, that asks whether a given graph is Hamiltonian (i.\,e.\ admits a Hamiltonian cycle), is one of Karp's famous NP-complete problems. In this paper we study graphs of bounded degree that are \emph{far} from being Hamiltonian, where a graph $G$ on $n$ vertices is \emph{far} from being Hamiltonian, if modifying a constant fraction of $n$ edges is necessary to make $G$ Hamiltonian. We give an explicit deterministic construction of a class of graphs of bounded degree that are locally Hamiltonian, but (globally) far from being Hamiltonian. Here, \emph{locally Hamiltonian} means that every subgraph induced by the neighbourhood of a small vertex set appears in some Hamiltonian graph. More precisely, we obtain graphs which differ in $\Theta(n)$ edges from any Hamiltonian graph, but non-Hamiltonicity cannot be detected in the neighbourhood of $o(n)$ vertices. Our class of graphs yields a class of hard instances for one-sided error property testers with linear query complexity. It is known that any property tester (even with two-sided error) requires a linear number of queries to test Hamiltonicity (Yoshida, Ito, 2010). This is proved via a randomised construction of hard instances. In contrast, our construction is deterministic. So far only very few deterministic constructions of hard instances for property testing are known. We believe that our construction may lead to future insights in graph theory and towards a characterisation of the properties hat are testable in the bounded-degree model. **

ACM/IEEE第23届模型驱动工程语言和系统国际会议，是模型驱动软件和系统工程的首要会议系列，由ACM-SIGSOFT和IEEE-TCSE支持组织。自1998年以来，模型涵盖了建模的各个方面，从语言和方法到工具和应用程序。模特的参加者来自不同的背景，包括研究人员、学者、工程师和工业专业人士。MODELS 2019是一个论坛，参与者可以围绕建模和模型驱动的软件和系统交流前沿研究成果和创新实践经验。今年的版本将为建模社区提供进一步推进建模基础的机会，并在网络物理系统、嵌入式系统、社会技术系统、云计算、大数据、机器学习、安全、开源等新兴领域提出建模的创新应用以及可持续性。
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** For a class $\mathcal{G}$ of graphs, the problem SUBGRAPH COMPLEMENT TO $\mathcal{G}$ asks whether one can find a subset $S$ of vertices of the input graph $G$ such that complementing the subgraph induced by $S$ in $G$ results in a graph in $\mathcal{G}$. We investigate the complexity of the problem when $\mathcal{G}$ is $H$-free for $H$ being a complete graph, a star, a path, or a cycle. We obtain the following results: - When $H$ is a $K_t$ (a complete graph on $t$ vertices) for any fixed $t\geq 1$, the problem is solvable in polynomial-time. This applies even when $\mathcal{G}$ is a subclass of $K_t$-free graphs recognizable in polynomial-time, for example, the class of $(t-2)$-degenerate graphs. - When $H$ is a $K_{1,t}$ (a star graph on $t+1$ vertices), we obtain that the problem is NP-complete for every $t\geq 5$. This, along with known results, leaves only two unresolved cases - $K_{1,3}$ and $K_{1,4}$. - When $H$ is a $P_t$ (a path on $t$ vertices), we obtain that the problem is NP-complete for every $t\geq 7$, leaving behind only two unresolved cases - $P_5$ and $P_6$. - When $H$ is a $C_t$ (a cycle on $t$ vertices), we obtain that the problem is NP-complete for every $t\geq 8$, leaving behind four unresolved cases - $C_4, C_5, C_6,$ and $C_7$. Further, we prove that these hard problems do not admit subexponential-time algorithms (algorithms running in time $2^{o(|V(G)|)}$), assuming the Exponential Time Hypothesis. A simple complementation argument implies that results for $\mathcal{G}$ are applicable for $\overline{\mathcal{G}}$, thereby obtaining similar results for $H$ being the complement of a complete graph, a star, a path, or a cycle. Our results generalize two main results and resolve one open question by Fomin et al. (Algorithmica, 2020). **

** In recent work, Gourv\`es, Lesca, and Wilczynski propose a variant of the classic housing markets model where the matching between agents and objects evolves through Pareto-improving swaps between pairs of adjacent agents in a social network. To explore the swap dynamics of their model, they pose several basic questions concerning the set of reachable matchings. In their work and other follow-up works, these questions have been studied for various classes of graphs: stars, paths, generalized stars (i.e., trees where at most one vertex has degree greater than two), trees, and cliques. For generalized stars and trees, it remains open whether a Pareto-efficient reachable matching can be found in polynomial time. In this paper, we pursue the same set of questions under a natural variant of their model. In our model, the social network is replaced by a network of objects, and a swap is allowed to take place between two agents if it is Pareto-improving and the associated objects are adjacent in the network. In those cases where the question of polynomial-time solvability versus NP-hardness has been resolved for the social network model, we are able to show that the same result holds for the network-of-objects model. In addition, for our model, we present a polynomial-time algorithm for computing a Pareto-efficient reachable matching in generalized star networks. Moreover, the object reachability algorithm that we present for path networks is significantly faster than the known polynomial-time algorithms for the same question in the social network model. **

** In 1979 Valiant introduced the complexity class VNP of p-definable families of polynomials, he defined the reduction notion known as p-projection and he proved that the permanent polynomial and the Hamiltonian cycle polynomial are VNP-complete under p-projections. In 2001 Mulmuley and Sohoni (and independently B\"urgisser) introduced the notion of border complexity to the study of the algebraic complexity of polynomials. In this algebraic machine model, instead of insisting on exact computation, approximations are allowed. This gives VNP the structure of a topological space. In this short note we study the set VNPC of VNP-complete polynomials. We show that the complement VNP \ VNPC lies dense in VNP. Quite surprisingly, we also prove that VNPC lies dense in VNP. We prove analogous statements for the complexity classes VF, VBP, and VP. The density of VNP \ VNPC holds for several different reduction notions: p-projections, border p-projections, c-reductions, and border c-reductions. We compare the relationship of the VNP-completeness notion under these reductions and separate most of the corresponding sets. Border reduction notions were introduced by Bringmann, Ikenmeyer, and Zuiddam (JACM 2018). Our paper is the first structured study of border reduction notions. **

** In order to facilitate the accesses of general users to knowledge graphs, an increasing effort is being exerted to construct graph-structured queries of given natural language questions. At the core of the construction is to deduce the structure of the target query and determine the vertices/edges which constitute the query. Existing query construction methods rely on question understanding and conventional graph-based algorithms which lead to inefficient and degraded performances facing complex natural language questions over knowledge graphs with large scales. In this paper, we focus on this problem and propose a novel framework standing on recent knowledge graph embedding techniques. Our framework first encodes the underlying knowledge graph into a low-dimensional embedding space by leveraging generalized local knowledge graphs. Given a natural language question, the learned embedding representations of the knowledge graph are utilized to compute the query structure and assemble vertices/edges into the target query. Extensive experiments were conducted on the benchmark dataset, and the results demonstrate that our framework outperforms state-of-the-art baseline models regarding effectiveness and efficiency. **

** Singleton arc consistency is an important type of local consistency which has been recently shown to solve all constraint satisfaction problems (CSPs) over constraint languages of bounded width. We aim to characterise all classes of CSPs defined by a forbidden pattern that are solved by singleton arc consistency and closed under removing constraints. We identify five new patterns whose absence ensures solvability by singleton arc consistency, four of which are provably maximal and three of which generalise 2-SAT. Combined with simple counter-examples for other patterns, we make significant progress towards a complete classification. **