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Ramsey Spanning Trees and their Applications [chapter]

Ittai Abraham, Shiri Chechik, Michael Elkin, Arnold Filtser, Ofer Neiman
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
Mendel and Naor [MN07] devised the so called Ramsey Partitions to address this problem, and showed the algorithmic applications of their techniques to approximate distance oracles and ranking problems.  ...  In this paper we study the natural extension of the metric Ramsey problem to graphs, and introduce the notion of Ramsey Spanning Trees.  ...  Our main application of Ramsey spanning trees is a compact routing scheme that has constant routing decision time and improved label size, see Section 1.1 for more details.  ... 
doi:10.1137/1.9781611975031.108 dblp:conf/soda/AbrahamCEFN18 fatcat:pz33dndq6rcc3mp7b67sxqrwje

Ramsey Spanning Trees and their Applications [article]

Ittai Abraham, Shiri Chechik, Michael Elkin, Arnold Filtser, Ofer Neiman
2017 arXiv   pre-print
Mendel and Naor 2007 devised the so called Ramsey Partitions to address this problem, and showed the algorithmic applications of their techniques to approximate distance oracles and ranking problems.  ...  In this paper we study the natural extension of the metric Ramsey problem to graphs, and introduce the notion of Ramsey Spanning Trees.  ...  Our main application of Ramsey spanning trees is a compact routing scheme that has constant routing decision time and improved label size, see Section 1.1 for more details.  ... 
arXiv:1707.08769v1 fatcat:vdotzere7bf3jdjxvhbylsvnmy

Covering Metric Spaces by Few Trees

Yair Bartal, Nova Fandina, Ofer Neiman, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
Tree covers and Ramsey tree covers have been studied by [15, 31, 19, 30, 38] , and have found several important algorithmic applications, e.g. routing and distance oracles.  ...  In this paper we devise efficient algorithms to construct tree covers and Ramsey tree covers for general, planar and doubling metrics.  ...  Acknowledgements We are grateful to Michael Elkin and Shay Solomon for fruitful discussions.  ... 
doi:10.4230/lipics.icalp.2019.20 dblp:conf/icalp/BartalFN19 fatcat:boc726yaxzdqhnv47tevxy6ykm

Page 3399 of Mathematical Reviews Vol. , Issue 86h [page]

1986 Mathematical Reviews  
H. (1-MEMP) Generalizations of the tree-complete graph Ramsey number. Graphs and applications (Boulder, Colo., 1982), 117-126, Wiley-Intersci. Publ., Wiley, New York, 1985.  ...  Given an undirected graph, the Minram algorithm starts by finding a spanning tree which defines a unique spanning arborescence.  ... 

Page 2132 of Mathematical Reviews Vol. , Issue 97D [page]

1997 Mathematical Reviews  
K. (1-RTG-OR; New Brunswick, NJ) Laplacian spectra and spanning trees of threshold graphs. (English summary) First International Colloquium on Graphs and Optimization (GOI), 1992 (Grimentz).  ...  of their degree sequences.  ... 

Covering Metric Spaces by Few Trees [article]

Yair Bartal, Nova Fandina, Ofer Neiman
2019 arXiv   pre-print
Tree covers and Ramsey tree covers have been studied by BLMN03,GKR04,CGMZ05,GHR06,MN07, and have found several important algorithmic applications, e.g. routing and distance oracles.  ...  In this paper we devise efficient algorithms to construct tree covers and Ramsey tree covers for general, planar and doubling metrics.  ...  Tree covers and Ramsey tree covers have been studied by [GKR04, BLMN05, CGMZ05, GHR06, MN07] , and are useful ingredients in important algorithmic applications such as routing and distance oracles.  ... 
arXiv:1905.07559v1 fatcat:uzmzxzj5cbgktfvteidavkoxia

Tree containment and degree conditions [article]

Maya Stein
2020 arXiv   pre-print
We survey results and open problems relating degree conditions with tree containment in graphs, random graphs, digraphs and hypergraphs, and their applications in Ramsey theory.  ...  Expansion and random graphs will be discussed in Section 6. Some of the above conjectures have direct applications in Ramsey theory, giving upper bounds on Ramsey numbers of trees.  ...  Ramsey numbers Both Conjecture 2.1 (the Erdős-Sós conjecture) and Conjecture 3.3 (the Loebl-Komlós-Sós conjecture) have a direct application in Ramsey theory.  ... 
arXiv:1912.04004v2 fatcat:tgw5raavandr3bkfamqlt7ers4

Page 1845 of Mathematical Reviews Vol. , Issue 83e [page]

1983 Mathematical Reviews  
The tree graph of G, denoted by I'(G), is the graph obtained as follows: the vertices of ['(G) are the spanning trees of G.  ...  [Rousseau, Cecil Clyde] Generalizations of a Ramsey result of Chvatal. The theory and applications of graphs ( Kalamazoo, Mich., 1980), pp. 351-361, Wiley, New York, 1981.  ... 

Page 2759 of Mathematical Reviews Vol. , Issue 2004d [page]

2004 Mathematical Reviews  
This article surveys some recent results on the generation of im- plicitly given hypergraphs and their applications in Boolean and integer programming, data mining, reliability theory, and combi- natorics  ...  The main results here are that non-z (mod /) dominating sets exist for every k >2 and z #1 (mod k) for all trees; and that non-z (mod k) dominating sets exist for every k > 4 and z # 1, 2, or 3 (mod k)  ... 

Page 980 of Mathematical Reviews Vol. 36, Issue 5 [page]

1968 Mathematical Reviews  
Sedlatek, Jifi 5021 Finite graphs and their spanning trees. (Czech and Russian summaries) Casopis Pést. Mat. 92 (1967), 338-342.  ...  Namely, given the complete graph C,, on n vertices and two fixed edges h, and h, in C,, it is shown that both sides of the equation are, but for a factor 4, equal to the number of spanning trees in C,,  ... 

Long cycles in locally expanding graphs, with applications [article]

Michael Krivelevich
2017 arXiv   pre-print
We provide sufficient conditions for the existence of long cycles in locally expanding graphs, and present applications of our conditions and techniques to Ramsey theory, random graphs and positional games  ...  Then whp every set of k ≤ δn vertices of G spans fewer than c 2 k edges. We now proceed to describe applications of our results. The first application is in the realm of Ramsey theory.  ...  The algorithm outputs a spanning forest F of G, where the connected components of G and of F coincide, and each component of F is a tree rooted at the first (according to σ) vertex of the corresponding  ... 
arXiv:1609.06851v2 fatcat:a5nia7hfdjdrtfn4h4aiz7hgae

Page 1061 of Mathematical Reviews Vol. 55, Issue 4 [page]

1978 Mathematical Reviews  
The author studies the number of distinct spanning trees in G containing F for certain classes of graphs G and uses the obtained results for construction of formulas for enumeration of all distinct spanning  ...  The authors make corrections to the statement and proof of Theorem 10, Corollary 10.1, Theorem 11 and Theorem 13 of their original paper [MR 52 #13470]. Homenko, N. P. [Homenko, M.  ... 

Bounded diameter arboricity

Martin Merker, Luke Postle
2018 Journal of Graph Theory  
As an application we show that every 6-edge-connected planar (multi)graph contains two edge-disjoint 18 19 -thin spanning trees.  ...  Moreover, we answer a question by Mütze and Peter leading to an improved lower bound on the density of globally sparse Ramsey graphs.  ...  In Section 3, as another application, we show the existence of ε-thin spanning trees in highly edge-connected planar graphs by investigating the bounded diameter arboricity for planar graphs of a certain  ... 
doi:10.1002/jgt.22416 fatcat:yh5ghdnbdjcwdnp7coojvhz3my

Page 6742 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
j=] j=] Based on known results concerning Ramsey numbers, some upper and lower bounds on Ramsey numbers can be directly derived using these properties.” Sey, !  ...  Summary: “For three kinds of chess-like knights, one on a triangle board and two on hexagon boards, the independence numbers for their knight graphs are considered.  ... 

Este, Padova, Italy: Dating the Iron Age Waterfront

John Meadows, Nicoletta Martinelli, Marie-Josée Nadeau, Elodia Bianchin Citton
2014 Radiocarbon: An International Journal of Cosmogenic Isotope Research  
Wiggle-match radiocarbon dating shows that one chronology spans the 10th and 9th centuries cal BC, and that the waterfront was probably built ∼800 cal BC.  ...  The second chronology apparently spans most of the 7th century cal BC, and is associated with a phase of construction about 2 centuries after the first.  ...  ACKNOWLEDGMENTS Research at Este was financed by the Ministero dell'Economia e Ministero per i Beni le Attività Culturali, through ARCUS SpA, its body supporting advancement of art, culture and performance  ... 
doi:10.1017/s0033822200049699 fatcat:pijjybzgtvchvntkvlfro6vu6q
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