scholarly journals Ramsey-Type Theorems for Spatial Graphs and Good Drawings

1998 ◽  
Vol 72 (1) ◽  
pp. 53-62 ◽  
Author(s):  
Seiya Negami
Keyword(s):  
Spatial Graphs ◽  
Ramsey Type

Ramsey-Type Theorem for Spatial Graphs

1998 ◽  
Vol 14 (1) ◽  
pp. 75-80 ◽  
Author(s):  
Seiya Negami
Keyword(s):  
Type Theorem ◽  
Spatial Graphs ◽  
Ramsey Type

scholarly journals A Ramsey-type problem on right-angled triangles in space

1996 ◽  
Vol 150 (1-3) ◽  
pp. 61-67 ◽  
Author(s):  
Miklós Bóna ◽  
Géza Tóth
Keyword(s):  
Type Problem ◽  
Ramsey Type

scholarly journals Reverse mathematics and a Ramsey-type König's Lemma

2012 ◽  
Vol 77 (4) ◽  
pp. 1272-1280 ◽  
Author(s):  
Stephen Flood
Keyword(s):  
Reverse Mathematics ◽  
Ramsey's Theorem ◽  
Weak Regularity ◽  
Ramsey’S Theorem ◽  
Ramsey Type ◽  
Weak König’S Lemma ◽  
König’S Lemma

AbstractIn this paper, we propose a weak regularity principle which is similar to both weak König's lemma and Ramsey's theorem. We begin by studying the computational strength of this principle in the context of reverse mathematics. We then analyze different ways of generalizing this principle.

scholarly journals Partitioning the Power Set of $[n]$ into $C_k$-free parts

10.37236/8385 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Eben Blaisdell ◽  
András Gyárfás ◽  
Robert A. Krueger ◽  
Ronen Wdowinski
Keyword(s):  
Upper Bound ◽  
Connected Graph ◽  
Type Problem ◽  
Color Class ◽  
Power Set ◽  
Ramsey Type ◽  
Partition Class ◽  
Cycle Path

We show that for $n \geq 3, n\ne 5$, in any partition of $\mathcal{P}(n)$, the set of all subsets of $[n]=\{1,2,\dots,n\}$, into $2^{n-2}-1$ parts, some part must contain a triangle — three different subsets $A,B,C\subseteq [n]$ such that $A\cap B,A\cap C,B\cap C$ have distinct representatives. This is sharp, since by placing two complementary pairs of sets into each partition class, we have a partition into $2^{n-2}$ triangle-free parts.  We also address a more general Ramsey-type problem: for a given graph $G$, find (estimate) $f(n,G)$, the smallest number of colors needed for a coloring of $\mathcal{P}(n)$, such that no color class contains a Berge-$G$ subhypergraph. We give an upper bound for $f(n,G)$ for any connected graph $G$ which is asymptotically sharp when $G$ is a cycle, path, or star. Additional bounds are given when $G$ is a $4$-cycle and when $G$ is a claw.

scholarly journals Optimal Factor Taxation under Wage Bargaining: A Dynamic Perspective

2008 ◽  
Vol 9 (2) ◽  
pp. 135-159 ◽  
Author(s):  
Erkki Koskela ◽  
Leopold von Thadden
Keyword(s):  
Steady State ◽  
General Equilibrium ◽  
Wage Bargaining ◽  
Labour Markets ◽  
Conflicting Demands ◽  
Imperfectly Competitive ◽  
Wage Tax ◽  
Dynamic Perspective ◽  
Capital Tax ◽  
Ramsey Type

Abstract We consider the issue of steady-state optimal factor taxation in a Ramsey-type dynamic general equilibrium setting with two distinct distortions: (i) taxes on capital and labour are the only available tax instruments for raising revenues and (ii) labour markets are subject to an inefficiency resulting from wage bargaining. If considered in isolation, the two distortions create conflicting demands on the wage tax, while calling for a zero capital tax. By combining the two distortions, we arrive at the conclusion that both instruments should be used, implying that the zero capital tax result in general is no longer valid under imperfectly competitive labour markets.

scholarly journals A Ramsey-type property in additive number theory

1985 ◽  
Vol 27 ◽  
pp. 5-10
Author(s):  
S. A. Burr ◽  
P. Erdös
Keyword(s):  
Number Theory ◽  
Positive Integer ◽  
Additive Number Theory ◽  
Additive Number ◽  
Large Positive Integer ◽  
Ramsey Type ◽  
Type Property ◽  
Positive Integers

Let A be a sequence of positive integers. Define P(A) to be the set of all integers representable as a sum of distinct terms of A. Note that if A contains a repeated value, we are free to use it as many times as it occurs in A. We call A complete if every sufficiently large positive integer is in P(A), and entirely complete if every positive integer is in P(A). Completeness properties have received considerable, if somewhat sporadic, attention over the years. See Chapter 6 of [3] for a survey.

Robot navigation algorithms using learned spatial graphs

Robotica ◽  
1986 ◽  
Vol 4 (2) ◽  
pp. 93-100 ◽  
Author(s):  
S. S. Iyengar ◽  
C. C. Jorgensen ◽  
S. V. N. Rao ◽  
C. R. Weisbin
Keyword(s):  
Robot Navigation ◽  
Sensor Data ◽  
Two Dimensional ◽  
Continuous Transition ◽  
Spatial Graph ◽  
Spatial Graphs ◽  
Navigation Algorithms ◽  
Sensor Information ◽  
Navigation Planning ◽  
Available Information

SUMMARYFinding optimal paths for robot navigation in a known terrain has been studied for some time but, in many important situations, a robot would be required to navigate in completely new or partially explored terrain. We propose a method of robot navigation which requires no pre-learned model, makes maximal use of available information, records and synthesizes information from multiple journeys, and contains concepts of learning that allow for continuous transition from local to global path optimality. The model of the terrain consists of a spatial graph and a Voronoi diagram. Using acquired sensor data, polygonal boundaries containing perceived obstacles shrink to approximate the actual obstacles surfaces, free space for transit is correspondingly enlarged, and additional nodes and edges are recorded based on path intersections and stop points. Navigation planning is gradually accelerated with experience since improved global map information minimizes the need for further sensor data acquisition. Our method currently assumes obstacle locations are unchanging, navigation can be successfully conducted using two-dimensional projections, and sensor information is precise.

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