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Note on Ramsey theorems for spatial graphs

Seiya Negami
2001 Theoretical Computer Science  
To show that Ramsey theorem for spatial graphs without local knots does not hold in general, we construct a spatial embedding of Kn;n which has no local knots on edges and which contains any subdivision  ...  This theorem can be regarded as a kind of "Ramsey theorems", which state that a su ciently large complete graph always includes a certain structure (see [2] for Ramsey theory).  ...  So, the natural question arises: does the Ramsey theorem with prescribed knot type or link type hold for spatial embeddings without local knots on edges?  ... 
doi:10.1016/s0304-3975(00)00242-5 fatcat:3i2woxmx7raefbob26cwbapqg4

Page 7565 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
Pavel Valtr (CZ-KARL-AM; Prague) 98m:05132 05C55 Negami, Seiya (J-YOKOED; Yokohama) Ramsey-type theorems for spatial graphs and good drawings. (English summary) J. Combin. Theory Ser.  ...  In this note, we establish the exact value of the bipartite Ramsey number b(P,,,.K.») for all integers m,n > 2, where P,,, denotes a path on m vertices.” 98m:05129 05C55 Karolyi, G.  ... 

Knots and links in spatial graphs: A survey

J.L. Ramírez Alfonsín
2005 Discrete Mathematics  
A recent area of research investigates the dependence (or independence) of the link types on the structure of the abstract graph G itself rather than on specific spatial representations of G.  ...  A spatial representation, R(G), of a graph G, is an embedded image of G in R 3 .  ...  In [41] , Negami showed that Ramsey theorem for spatial graphs without local knots does not hold in general.  ... 
doi:10.1016/j.disc.2004.07.035 fatcat:ncvossm7nfdfzdn4zz2wxeohme

Page 3818 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
Andras Gyarfas (H-AOS-C; Budapest) 2002f:05113 05C55 Negami, Seiya (J-YOKOTEH; Yokohama) Note on Ramsey theorems for spatial graphs.  ...  Summary: “To show that a Ramsey theorem for spatial graphs without local knots does not hold in general, we construct a spatial embedding of K,,,, which has no local knots on edges and which contains any  ... 

Topological Graph Theory from Japan

Seiya NEGAMI
2001 Interdisciplinary Information Sciences  
This is a survey of studies on topological graph theory developed by Japanese people in the recent two decades and presents a big bibliography including almost all papers written by Japanese topological  ...  graph theorists.  ...  Ramsey theorems for spatial graphs An embedding f : G → R 3 of a graph G into the 3-space R 3 is called a spatial embedding of G and its image f(G) is called a spatial graph.  ... 
doi:10.4036/iis.2001.99 fatcat:6qxw75knznei5gjuzlfk6inxre

Author index volume 263 (2001)

2001 Theoretical Computer Science  
Matsui, NP-completeness for calculating power indices of weighted majority games (1}2) 305}310 Negami, S., Note on Ramsey theorems for spatial graphs (1}2) 205}210 Nielsen, F., On point covers of c-oriented  ...  Tuza, Ramsey numbers for tournaments (1}2) 75} 85 Martin, B., A simulation of cellular automata on hexagons by cellular automata on rings (1}2) 231}234 Matsui, T., see Y.  ... 
doi:10.1016/s0304-3975(01)00283-3 fatcat:xv3da2ixwzf4pfp47jgune5zg4

Page 7230 of Mathematical Reviews Vol. , Issue 2003i [page]

2003 Mathematical Reviews  
It is noted that this theorem characterizes the group U and also noted that the theorem is false if restricted to games in which only finitely many options are permitted.  ...  In particular, the value q¢ mentioned above is the clique number of the random graph on n vertices with edge-probability }. The same answer is given for two other Ramsey games. N.N. Petrov (St.  ... 

Occupancy fraction, fractional colouring, and triangle fraction [article]

Ewan Davies, Rémi de Joannis de Verclos, Ross J. Kang, François Pirot
2020 arXiv   pre-print
Given ε>0, there exists f_0 such that, if f_0 ≤ f ≤Δ^2+1, then for any graph G on n vertices of maximum degree Δ in which the neighbourhood of every vertex in G spans at most Δ^2/f edges, (i) an independent  ...  One may view these as stronger versions of results of Ajtai, Komlós and Szemerédi (1981) and Shearer (1983). The proofs use a tight analysis of the hard-core model.  ...  We are grateful to Matthew Jenssen, Will Perkins and Barnaby Roberts for helpful discussions, particularly in relation to the analysis in Section 3.  ... 
arXiv:1812.11152v2 fatcat:qnyxitgqlvbxrknimbnxvlgufu

Decidability of Definability

Manuel Bodirsky, Michael Pinsker, Todor Tsankov
2013 Journal of Symbolic Logic (JSL)  
We show decidability of this problem for all structures Γ that have a first-order definition in an ordered homogeneous structure Δ with a finite relational signature whose age is a Ramsey class and determined  ...  Our proof makes use of universal algebraic and model theoretic concepts, Ramsey theory, and a recent characterization of Ramsey classes in topological dynamics.  ...  We would like to thank the referees for their comments.  ... 
doi:10.2178/jsl.7804020 fatcat:la3j7odll5fyrnqripall56s5q

Decidability of Definability

Manuel Bodirsky, Michael Pinsker, Todor Tsankov
2011 2011 IEEE 26th Annual Symposium on Logic in Computer Science  
We show decidability of this problem for all structures Γ that have a first-order definition in an ordered homogeneous structure ∆ with a finite relational signature whose age is a Ramsey class and determined  ...  Our proof makes use of universal algebraic and model theoretic concepts, Ramsey theory, and a recent characterization of Ramsey classes in topological dynamics.  ...  We would like to thank the referees for their comments.  ... 
doi:10.1109/lics.2011.11 dblp:conf/lics/BodirskyPT11 fatcat:xob3ubxjqzd5tfaqdm7qukstze

Page 4873 of Mathematical Reviews Vol. , Issue 84m [page]

1984 Mathematical Reviews  
’s theorem on planar graphs—an open problem (pp. 230-241); J.  ...  Rosenstiehl, A discriminatory theorem of Kuratowski subgraphs (pp. 214-222); Wojciech Rytter, A note on the complexity of traversing a labyrinth (pp. 223-229); Horst Sachs, On a spatial analogue of Kuratowski  ... 

Fractional chromatic number, maximum degree and girth [article]

François Pirot, Jean-Sébastien Sereni
2021 arXiv   pre-print
We introduce a new method for computing bounds on the independence number and fractional chromatic number of classes of graphs with local constraints, and apply this method in various scenarios.  ...  a breakthrough in Ramsey theory.  ...  Since the seminal result of Ramsey [22] , the branch of combinatorics now called "Ramsey Theory" has known an ever increasing range of interest from the community. Theorem 1 (Ramsey, 1930) .  ... 
arXiv:1904.05618v6 fatcat:mnqs5soj3vd3xmtphnxmlkskqa

Occupancy fraction, fractional colouring, and triangle fraction

Ewan Davies, Rémi Joannis de Verclos, Ross J. Kang, François Pirot
2021 Journal of Graph Theory  
Given ε > 0 , there exists f 0 such that, if f 0 ≤ f ≤ Δ 2 + 1 , then for any graph G on n vertices of maximum degree Δ in which the neighbourhood of every vertex in G spans at most Δ 2 ∕ f edges, (i)an  ...  One may view these as stronger versions of results of Ajtai, Komlós and Szemerédi and Shearer. The proofs use a tight analysis of the hard-core model.  ...  We are thankful to the anonymous referees for their thorough reading and helpful comments.  ... 
doi:10.1002/jgt.22671 pmid:34248256 pmcid:PMC8252119 fatcat:wqizrr7f2vcsdbxfhyjwef7wby

Graph structure via local occupancy [article]

Ewan Davies, Ross J. Kang, François Pirot, Jean-Sébastien Sereni
2020 arXiv   pre-print
It pivots on a property we call local occupancy, giving a clean separation between the methods for deriving graph structure with probabilistic information and verifying the requisite probabilistic information  ...  graphs in terms of local sparsity, treating for example graphs of bounded local edge density, of bounded local Hall ratio, and of bounded clique number.  ...  Acknowledgements We would like to thank Alistair Sinclair, Fotis Iliopoulos, and Charlie Carlson for insightful discussions.  ... 
arXiv:2003.14361v1 fatcat:vkyt7iw7cfcf7pbmhdjk4rj5cm

Page 435 of Mathematical Reviews Vol. , Issue 85b [page]

1985 Mathematical Reviews  
These are realized as 4-trees on twelve points. Theorems are presented for constructing these graphs and other J-equivalent graphs of higher orders. A comparison with M.  ...  J. (1-MEMP); Sheehan, John (4-ABER) Tree Ramsey minimal graphs. Proceedings of the thirteenth Southeastern conference on combinatorics, graph theory and computing (Boca Raton, Fla., 1982). Congr.  ... 
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