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Probability of diameter two for Steinhaus graphs

Neal Brand, Stephen Curran, Sajal Das, Tom Jacob
1993 Discrete Applied Mathematics  
Under reasonable conditions it is shown that the probability measure of the set of Steinhaus graphs with diameter two approaches 1 as the number of vertices in the graph approaches infinity.  ...  Jacob, Probability of diameter two for Steinhaus graphs, Discrete Applied Mathematics 41 (1993) 1655171.  ...  Acknowledgement We would like to thank Narsingh Deo at the University of Central Florida for introducing us to Steinhaus graphs.  ... 
doi:10.1016/0166-218x(93)90036-n fatcat:72fqc55r3ndc5bfcpwlqkxa7au

2-connected and 2-edge-connected Steinhaus graphs

Dongju Kim, Daekeun Lim
2002 Discrete Mathematics  
The possible generating strings of 2-connected and 2-edge-connected Steinhaus graphs are classiÿed.  ...  The numbers of 2-connected and 2-edge-connected Steinhaus graphs with n vertices are determined for n ¿ 6.  ...  Dym  a Ä cek for his invaluable comments concerning an earlier draft of the manuscript.  ... 
doi:10.1016/s0012-365x(01)00468-x fatcat:vsnbpgqny5d5vcysv3d3i4drcu

Characterizations of bipartite Steinhaus graphs

Gerard J. Chang, Bhaskar DasGupta, Wayne M. Dymàček, Martin Fürer, Matthew Koerlin, Yueh-Shin Lee, Tom Whaley
1999 Discrete Mathematics  
Also, we exhibit a lower bound, which is achieved infinitely often, for the number of bipartite Steinhaus graphs.  ...  We characterize bipartite Steinhaus graphs in three ways by partitioning them into four classes and we describe the color sets for each of these classes.  ...  Molluzzo [ 171 was the first to form graphs from Steinhaus triangles, but he examined the complements of what we call Steinhaus graphs.  ... 
doi:10.1016/s0012-365x(98)00282-9 fatcat:ydih3f4dfzfcbochxmwsdfezg4

Page 8629 of Mathematical Reviews Vol. , Issue 2001M [page]

2001 Mathematical Reviews  
and that for n > 10, all complements of Steinhaus graphs on n vertices are non-planar.”  ...  Summary: “The characterization of Steinhaus graphs with a given property is often quite difficult. This is not the case, however, with planar Steinhaus graphs.  ... 

Generating strings for bipartite Steinhaus graphs

Wayne M. Dymàček, Tom Whaley
1995 Discrete Mathematics  
Let b(n) be the number of bipartite Steinhaus graphs with n vertices. We show that bin) satisfies the recurrence, b(2)=2, b(3)=4, and for k>~2, b(2k+ 1)=2b(k+ 1)+ 1, b(2k) = b(k) + b(k + 1).  ...  Thus b(n) <<, ~zn -~ with equality when n is one more than a power of two.  ...  The complements of Steinhaus graphs were further studied in [5] and conditions and a conjecture on the existence of regular Steinhaus graphs were given in [1] .  ... 
doi:10.1016/0012-365x(93)e0211-l fatcat:t3h7vrw5mvabxeqnjrfgxdoocu

Page 2260 of Mathematical Reviews Vol. , Issue 88e [page]

1988 Mathematical Reviews  
An unbounded interval graph is the intersection graph of a fam- ily of halflines in R'; the authors show that they are precisely the triangulated graphs whose complements are bipartite.  ...  A Steinhaus graph 05 COMBINATORICS 2260 has a Steinhaus triangle as the upper triangular part of its sym- metric adjacency matrix.  ... 

Page 1779 of Mathematical Reviews Vol. , Issue 93d [page]

1993 Mathematical Reviews  
He also shows that the ratio of the number of Steinhaus graphs of order n whose complements have diameter 2 to the total number of Steinhaus graphs of order n approaches | as n goes to infinity.  ...  Numer. 76 (1990), 7- 14; MR 92h:05050] showed that almost all Steinhaus graphs have 05C Graph theory 934:05051 diameter at most 3 and conjectured that the ratio of the number of Steinhaus graphs of order  ... 

Parity-regular Steinhaus graphs

Maxime Augier, Shalom Eliahou
2008 Mathematics of Computation  
Steinhaus graphs on n vertices are certain simple graphs in bijective correspondence with binary {0,1}-sequences of length n − 1.  ...  A conjecture of Dymacek in 1979 states that the only nontrivial regular Steinhaus graphs are those corresponding to the periodic binary sequences 110...110 of any length n − 1 = 3m.  ...  The second author gratefully acknowledges partial support from the Fonds National Suisse de la Recherche Scientifique during the preparation of this paper.  ... 
doi:10.1090/s0025-5718-07-02063-7 fatcat:hoshe6slzbdhjd7jbpzsi7pf5i

Page 6443 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
The authors prove that every simple graph is an induced subgraph of some Steinhaus graph. Let Ns(G) =r [resp.  ...  N;(G) = s] be the smallest integer such that G is a subgraph [resp. induced subgraph] of a Steinhaus graph with r [resp. s] vertices.  ... 

Page 1307 of Mathematical Reviews Vol. , Issue 84d [page]

1984 Mathematical Reviews  
These results continue a study of such complements introduced by J. C.  ...  Hoede (Enschede) 24d: O60 Dymacek, Wayne M. 84d:05151 of Steinhaus graphs. Discrete Math. 37 (1981), no. 2-3, 167-180.  ... 

Page 726 of Mathematical Reviews Vol. , Issue 98B [page]

1998 Mathematical Reviews  
In addition, it is shown that the complement of a knapsack graph is a knapsack graph, knap- sack graphs themselves are characterized, and helpful conversion algorithms are provided.  ...  A Steinhaus graph is one whose adjacency matrix satisfies a; ; + Gj j+1 =4)+1,;+1 (mod 2). The matrix is thus determined by the first row. The authors consider random Steinhaus graphs.  ... 

Steinhaus Sets and Jackson Sets [article]

Su Gao, Arnold W. Miller, William A. R. Weiss
2006 arXiv   pre-print
We prove that there does not exist a subset of the plane S that meets every isometric copy of the vertices of the unit square in exactly one point.  ...  We give a complete characterization of all three point subsets F of the reals such that there does not exists a set of reals S which meets every isometric copy of F in exactly one point.  ...  Then B ∪ C is the complement of D * (mod M) in {0, . . . , M − 1}. Assume that a Steinhaus set of period M for (1, 1, 4k+3) existed. Then by Proposition 2.14 there are x 1 , . .  ... 
arXiv:math/0603235v1 fatcat:dltmotnhpzgc5gypw6z6v2d5ua

Page 3767 of Mathematical Reviews Vol. , Issue 91G [page]

1991 Mathematical Reviews  
The authors extend the Hahn-Banach and Banach-Steinhaus theorems to convex processes.  ...  Vietnam. 5 (1980), no. 1, 161-168; MR 83d:47070] on the Banach-Steinhaus theorem in a more general setting: X is a barreled space, Y is a locally convex Hausdorff space and I a family of cone convex multifunctions  ... 

Kaleidoscopical configurations

Igor Protasov, Ksenia Protasova
2014 Journal of Mathematical Sciences  
A subset A of X is called a kaleidoscopical configuration if there is a coloring χ : X → κ (i.e. a mapping of X onto a cardinal κ) such that the restriction χ|gA is a bijection for each g ∈ G.  ...  We survey some recent results on kaleidoscopical configurations in metric spaces considered as G-spaces with respect to the groups of its isometries and in groups considered as left regular G-spaces. 2010  ...  These graphs define the kaleidoscopical hypergraphs (V, {B(v, 1) : v ∈ V }) and can be considered as the graph counterparts of the Hamming codes [10] .  ... 
doi:10.1007/s10958-014-1917-9 fatcat:5qbvvhhtzrhdrdxuolg4wr6iwq

Page 446 of Mathematical Reviews Vol. 45, Issue 2 [page]

1973 Mathematical Reviews  
open sets of the graph of u are Baire sets, then uw is continuous.  ...  The author proves the following convenient proposition: If ® is a non-empty face of X and if the complement of ® in X is an F, set, then ® contains a weakly exposed face of the first class.  ... 
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