1,720,982 research outputs found
Automated Discharging Arguments for Density Problems in Grids
No full textDischarging arguments demonstrate a connection between local structure and global averages. This makes it an effective tool for proving lower bounds on the density of special sets in infinite grids. How-ever, the minimum density of an identifying code in the hexagonal grid remains open, with an upper bound of 37 ≈ 0.428571 and a lower bound of 512 ≈ 0.416666. We present a new framework for pro-ducing discharging arguments using an algorithm. This algorithm replaces the lengthy case analysis of human-written discharging arguments with a linear program that produces the best possible lower bound using the specified set of discharging rules. We use this framework to present a lower bound of 23 55 ≈ 0.41818 on the density of an identifying code in the hexagonal grid, and also find several sharp lower bounds for variations on identifying codes in the hexagonal, square, triangular, and pentagonal grids. We also present a new method to find matching upper bounds. ∗Pages 1-10 of this PDF contain the extended abstract, with some figures, tables, and proofs appearing in appendices (pp
Automorphism Groups and Adversarial Vertex Deletions
No full textAny finite group can be encoded as the automorphism group of an unlabeled simple graph. Recently Hartke, Kolb, Nishikawa, and Stolee (2010) demonstrated a construction that allows any ordered pair of finite groups to be represented as the automorphism group of a graph and a vertex-deleted subgraph. In this note, we describe a generalized scenario as a game between a player and an adversary: An adversary provides a list of finite groups and a number of rounds. The player constructs a graph with automorphism group isomorphic to the first group. In the following rounds, the adversary selects a group and the player deletes a vertex such that the automorphism group of the corresponding vertex-deleted subgraph is isomorphic to the selected group. We provide a construction that allows the player to appropriately respond to any sequence of challenges from the adversary. Automorphisms of graphs are incredibly unstable. The slightest perturbation of the graph can greatly change the automorphism group. In this note, we show there exist graphs whose automorphism groups can change dramatically under certain sequences of vertex deletions. We consider undirected, unlabeled, and simple graphs, denoted F, G, or H, and finite groups, denote
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
ORDERED RAMSEY NUMBERS OF LOOSE PATHS AND MATCHINGS
No full textFor a k-uniform hypergraph G with vertex set {1,..., n}, the ordered Ramsey number ORt(G) is the least integer N such that every t-coloring of the edges of the complete k-uniform graph on vertex set {1,..., N} contains a monochromatic copy of G whose vertices follow the prescribed order. Due to this added order restriction, the ordered Ramsey numbers can be much larger than the usual graph Ramsey numbers. We determine that the ordered Ramsey numbers of loose paths under a monotone order grows as a tower of height two less than the maximum degree in terms of the number of edges. We also extend theorems of Conlon, Fox, Lee, and Sudakov [Ordered Ramsey numbers, arXiv:1410.5292] on the ordered Ramsey numbers of 2-uniform matchings to provide upper bounds on the ordered Ramsey number of k-uniform matchings under certain orderings
RAMSEY NUMBERS FOR PARTIALLY-ORDERED SETS
No full textWe present a refinement of Ramsey numbers by considering graphs with a partial ordering on their vertices. This is a natural extension of the ordered Ramsey numbers. We formalize situations in which we can use arbitrary families of partially-ordered sets to form host graphs for Ramsey problems. We explore connections to well studied Turán-type problems in partially-ordered sets, particularly those in the Boolean lattice. We find a strong difference between Ramsey numbers on the Boolean lattice and ordered Ramsey numbers when the partial ordering on the graphs have large antichains
On Choosability with Separation of Planar Graphs with Forbidden Cycles
No full textWe study choosability with separation which is a constrained version of list coloring of graphs. A (k, d)-list assignment L of a graph G is a function that assigns to each vertex v a list L(v) of at least k colors and for any adjacent pair xy, the lists L(x) and L(y) share at most d colors. A graph G is (k, d)-choosable if there exists an L-coloring of G for every (k, d)-list assignment L. This concept is also known as choosability with separation. We prove that planar graphs without 4-cycles are (3, 1)-choosable and that planar graphs without 5-cycles and 6-cycles are (3, 1)-choosable. In addition, we give an alternative and slightly stronger proof that triangle-free planar graphs are (3, 1)-choosable.
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