On Linked Spatial Representations

2001 ◽  
Vol 10 (01) ◽  
pp. 143-150 ◽  
Author(s):  
J. L. Ramírez Alfonsín
Keyword(s):  
Positive Integer ◽  
Complete Graph ◽  
Spatial Representation ◽  
Oriented Matroids ◽  
Spatial Representations ◽  
Cyclic Polytope ◽  
Combinatorial Description

What is the smallest positive integer m=m(L) such that every linear spatial representation of the complete graph with n vertices, n≥m contain cycles isotopic to link L? In this paper, we show that [Formula: see text]. The proof uses the well-known cyclic polytope and its combinatorial description in terms of oriented matroids.

scholarly journals From Which Direction Does the Empire Strike (Back)?

2021 ◽  
Vol 12 ◽  
Author(s):  
Katharina Theresa Halicki ◽  
Moritz Ingendahl ◽  
Maren Mayer ◽  
Melvin John ◽  
Marcel Raphael Schreiner ◽  
...  
Keyword(s):  
Opposite Direction ◽  
Spatial Representation ◽  
Future Research ◽  
Spatial Representations ◽  
The Right ◽  
Attack And Defense

In cultures with left-right-script, agentic behavior is mentally represented as following a left-to-right trajectory, an effect referred to as the Spatial Agency Bias (SAB, Suitner and Maass, 2016). In this research, we investigated whether spatial representations of activities are universal across activities by analyzing the opposite concepts of “attack” and “defense”. Both behaviors involve similar actions (e.g., fighting) but may differ in perceived agency. Moreover “defense” is necessarily always a response to an attack and may therefore be represented by a trajectory in the opposite direction. Two studies found the classic SAB for activities representing attacking but a reduction (Study 1) and reversal (Study 2) for activities involving defense. Although the spatial representation of defense on the right was much weaker and less unequivocal than that of attack on the left, the results suggest that the spatial representations of defense and attack are located in different positions. Apparently not all actors and all activities are spatially represented on the left with a left-to-right trajectory but position and direction depend on the perceived agency. Directions for future research and applications of our findings are discussed.

A study on distance in graph complement

2020 ◽  
Vol 12 (03) ◽  
pp. 2050045
Author(s):  
A. Chellaram Malaravan ◽  
A. Wilson Baskar
Keyword(s):  
Positive Integer ◽  
Complete Graph ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The aim of this paper is to determine radius and diameter of graph complements. We provide a necessary and sufficient condition for the complement of a graph to be connected, and determine the components of graph complement. Finally, we completely characterize the class of graphs [Formula: see text] for which the subgraph induced by central (respectively peripheral) vertices of its complement in [Formula: see text] is isomorphic to a complete graph [Formula: see text], for some positive integer [Formula: see text].

scholarly journals A survey of qualitative spatial representations

2013 ◽  
Vol 30 (1) ◽  
pp. 106-136 ◽  
Author(s):  
Juan Chen ◽  
Anthony G. Cohn ◽  
Dayou Liu ◽  
Shengsheng Wang ◽  
Jihong Ouyang ◽  
...  
Keyword(s):  
Spatial Representation ◽  
Spatial Databases ◽  
Robot Navigation ◽  
Spatial Relations ◽  
Spatial Representations ◽  
Language Understanding ◽  
Different Types ◽  
Qualitative Spatial Representation ◽  
Autonomous Robot Navigation ◽  
Future Work

AbstractRepresentation and reasoning with qualitative spatial relations is an important problem in artificial intelligence and has wide applications in the fields of geographic information system, computer vision, autonomous robot navigation, natural language understanding, spatial databases and so on. The reasons for this interest in using qualitative spatial relations include cognitive comprehensibility, efficiency and computational facility. This paper summarizes progress in qualitative spatial representation by describing key calculi representing different types of spatial relationships. The paper concludes with a discussion of current research and glimpse of future work.

scholarly journals TILING DIRECTED GRAPHS WITH TOURNAMENTS

2018 ◽  
Vol 6 ◽  
Author(s):  
ANDRZEJ CZYGRINOW ◽  
LOUIS DEBIASIO ◽  
THEODORE MOLLA ◽  
ANDREW TREGLOWN
Keyword(s):  
Positive Integer ◽  
Directed Graph ◽  
Complete Graph ◽  
Directed Graphs ◽  
Type Result ◽  
Vertex Disjoint

The Hajnal–Szemerédi theorem states that for any positive integer $r$ and any multiple $n$ of $r$, if $G$ is a graph on $n$ vertices and $\unicode[STIX]{x1D6FF}(G)\geqslant (1-1/r)n$, then $G$ can be partitioned into $n/r$ vertex-disjoint copies of the complete graph on $r$ vertices. We prove a very general analogue of this result for directed graphs: for any positive integer $r$ with $r\neq 3$ and any sufficiently large multiple $n$ of $r$, if $G$ is a directed graph on $n$ vertices and every vertex is incident to at least $2(1-1/r)n-1$ directed edges, then $G$ can be partitioned into $n/r$ vertex-disjoint subgraphs of size $r$ each of which contain every tournament on $r$ vertices (the case $r=3$ is different and was handled previously). In fact, this result is a consequence of a tiling result for standard multigraphs (that is multigraphs where there are at most two edges between any pair of vertices). A related Turán-type result is also proven.

scholarly journals Distal CA1 maintains a more coherent spatial representation than proximal CA1 when local and global cues conflict

2020 ◽  
Author(s):  
Sachin S. Deshmukh
Keyword(s):  
Entorhinal Cortex ◽  
Spatial Representation ◽  
Reference Frames ◽  
Sensory Information ◽  
Spatial Representations ◽  
Transverse Axis ◽  
Medial Entorhinal Cortex ◽  
Spatial Selectivity ◽  
Functional Differences ◽  
Cortical Projections

AbstractEntorhinal cortical projections show segregation along the transverse axis of CA1, with the medial entorhinal cortex (MEC) sending denser projections to proximal CA1 (pCA1) and the lateral entorhinal cortex (LEC) sending denser projections to distal CA1 (dCA1). Previous studies have reported functional segregation along the transverse axis of CA1 correlated with the functional differences in MEC and LEC. pCA1 shows higher spatial selectivity than dCA1 in these studies. We employ a double rotation paradigm, which creates an explicit conflict between local and global cues, to understand differential contributions of these reference frames to the spatial code in pCA1 and dCA1. We show that pCA1 and dCA1 respond differently to this local-global cue conflict. pCA1 shows incoherent response consistent with the strong conflicting inputs it receives from MEC and distal CA3 (dCA3). In contrast, dCA1 shows a more coherent rotation with global cues. In addition, pCA1 and dCA1 display comparable levels of spatial selectivity in this study. This finding differs from the previous studies, perhaps due to richer sensory information available in our behavior arena. Together these observations indicate that the functional segregation along proximodistal axis of CA1 is not merely of the amount of spatial selectivity but that of the nature of the different inputs utilized to create and anchor spatial representations.

scholarly journals A Note on Odd Cycle-Complete Graph Ramsey Numbers

10.37236/1662 ◽  
2001 ◽  
Vol 9 (1) ◽  
Author(s):  
Benny Sudakov
Keyword(s):  
Positive Integer ◽  
Complete Graph ◽  
Upper Bound ◽  
Short Note ◽  
Ramsey Number ◽  
Ramsey Numbers ◽  
Odd Cycle

The Ramsey number $r(C_l, K_n)$ is the smallest positive integer $m$ such that every graph of order $m$ contains either cycle of length $l$ or a set of $n$ independent vertices. In this short note we slightly improve the best known upper bound on $r(C_l, K_n)$ for odd $l$.

scholarly journals Un método algoritmo para el cálculo del número baricéntrico de Ramsey para el grafo estrella

2018 ◽  
Vol 36 (2) ◽  
pp. 169-183
Author(s):  
Felicia Villarroel ◽  
J. Figueroa ◽  
H. Márquez ◽  
A. Anselmi
Keyword(s):  
Finite Group ◽  
Positive Integer ◽  
Complete Graph ◽  
Ramsey Number ◽  
Combinatorial Theory ◽  
Star Graph ◽  
Definition Of

Let G be an abelian finite group and H be a graph. A sequence in G, with length al least two, is barycentric if it contains an ”average” element of its terms. Within the context of these sequences, one defines the barycentric Ramsey number, denoted by BR(H, G), as the smallest positive integer t such that any coloration of the edges of the complete graph Kt with elements of G produces a barycentric copy of the graph H. In this work we present a method based on the combinatorial theory and on the definition of barycentric Ramsey for calculating exact values of the above metioned constant, for some small graphs where the order is less than or equal to 8. We will exemplify the case where H is the star graph K1,k, and where G is the cyclical group Zn, with 3 ≤ n ≤ 11 and 3 ≤ k ≤ n.

Ramsey Problems with Bounded Degree Spread

1993 ◽  
Vol 2 (3) ◽  
pp. 263-269 ◽  
Author(s):  
G. Chen ◽  
R. H. Schelp
Keyword(s):  
Positive Integer ◽  
Complete Graph ◽  
Maximum Degree ◽  
Minimum Degree ◽  
Bipartite Graphs ◽  
Bounded Degree ◽  
Monochromatic Copy

Let k be a positive integer, k ≥ 2. In this paper we study bipartite graphs G such that, for n sufficiently large, each two-coloring of the edges of the complete graph Kn gives a monochromatic copy of G, with some k of its vertices having the maximum degree of these k vertices minus the minimum degree of these k vertices (in the colored Kn) at most k − 2.

scholarly journals Linear embeddings of K9 are triple linked

2014 ◽  
Vol 23 (03) ◽  
pp. 1420001 ◽  
Author(s):  
Ramin Naimi ◽  
Elena Pavelescu
Keyword(s):  
Complete Graph ◽  
Oriented Matroids ◽  
Linear Embedding ◽  
Three Components

We use the theory of oriented matroids to show that any linear embedding of K9, the complete graph on nine vertices, into 3-space contains a non-split link with three components. This shows that Sachs' conjecture on linear, linkless embeddings of graphs, whether true or false, does not extend to 3-links.

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