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Page 66 of Mathematical Reviews Vol. , Issue 90A [page]

1990 Mathematical Reviews  
A. (1-PRRP) Two Hamilton cycles in bipartite reflective Kneser graphs. Proceedings of the First Japan Conference on Graph Theory and Applications (Hakone, 1986).  ...  RG, ; is the bipartite graph in which the vertices are the i- and j- subsets of {0,---, i+ — 1} and in which two vertices are adjacent if and only if one is a subset of the other.  ... 

Page 5392 of Mathematical Reviews Vol. , Issue 89J [page]

1989 Mathematical Reviews  
Quintana, Two Hamilton cycles in bipartite reflective Kneser graphs (pp. 63-70); Chai Ling Deng and Chong Keang Lim, A result on generalized Latin rectangles (pp. 71-80); Paul Erdés, Problems and results  ...  Hobbs, Cycle-minimal graphs and vertices of low degree (pp. 125-130); Rhys Price Jones, A computer representation for graph theory knowledge (pp. 131- 136); Stephen Hedetniemi and Renu Laskar, A bipartite  ... 

Combinatorial Gray codes-an updated survey [article]

Torsten Mütze
2022 arXiv   pre-print
A combinatorial Gray code for a class of objects is a listing that contains each object from the class exactly once such that any two consecutive objects in the list differ only by a 'small change'.  ...  We also elaborate on the connections to closely related problems in graph theory, algebra, order theory, geometry and algorithms, which embeds this research area into a broader context.  ...  In the resulting cyclic Gray codes, any two consecutive bitstrings differ in at most 4 positions. 4.6. Bipartite Kneser graphs and Kneser graphs.  ... 
arXiv:2202.01280v1 fatcat:dnjvd2zih5dxrgs3vrwsfyhafi

Problems in Algebraic Combinatorics

C. D. Godsil
1995 Electronic Journal of Combinatorics  
This is a list of open problems, mainly in graph theory and all with an algebraic flavour. Except for 6.1, 7.1 and 12.2 they are either folklore, or are stolen from other people.  ...  Hamilton Cycles We consider the existence of Hamilton cycles in vertex transitive graphs. Ignoring K 2 , there are only four known vertex transitive graphs without Hamilton cycles.  ...  Witte [49] has proved that all Cayley graphs of p-groups have Hamilton cycles. For a survey of results on Hamilton cycles in Cayley graphs see, e.g., [50] .  ... 
doi:10.37236/1224 fatcat:etalsageu5awhdkehlcmt3uln4

Graphs as navigational infrastructure for high dimensional data spaces

C. B. Hurley, R. W. Oldford
2011 Computational statistics (Zeitschrift)  
These are connected to known results in graph theory and the graph theoretic results applied to the problem of visualizing high-dimensional data.  ...  We propose using graph theoretic results to develop an infrastructure that tracks movement from a display of one set of variables to another.  ...  Also related to bipartite graphs is the following result from Pike (1995) . If G is bipartite and (2k+1) regular and Hamilton decomposable, then so is L(G).  ... 
doi:10.1007/s00180-011-0228-6 fatcat:v6wmxh3vq5agpfw3widxpd7yji

Master index of volumes 71–80

1990 Discrete Mathematics  
Quintana, Two hamilton cycles in bipartite reflective Kneser graphs Deng, C-L. and C-K.  ...  Witte, Flows in circulant graphs of odd order are sums of Hamilton cycles Loebl, M. and S.  ... 
doi:10.1016/0012-365x(90)90304-z fatcat:tp4gu4hk2fbrdawvvu4vcsupii

Trimming and gluing Gray codes

Petr Gregor, Torsten Mütze
2018 Theoretical Computer Science  
Rephrased in terms of graph theory, our results establish the existence of (almost) Hamilton cycles in the subgraph of the n-dimensional cube Q_n induced by all levels [k,l].  ...  ,k}, has a Hamilton cycle. We also prove an approximate version of this generalized conjecture, showing that this graph has a cycle that visits a (1-o(1))-fraction of all vertices.  ...  Acknowledgements The authors thank Jiří Fink, Jerri Nummenpalo and Robert Šámal for several stimulating discussions about the problems discussed in this paper.  ... 
doi:10.1016/j.tcs.2017.12.003 fatcat:rgdurlmhy5aqlfpzsuw3m5jf4u

The Hamilton compression of highly symmetric graphs [article]

Petr Gregor, Arturo Merino, Torsten Mütze
2022 arXiv   pre-print
We refer to the maximum k for which there exists a k-symmetric Hamilton cycle in G as the Hamilton compression of G.  ...  We say that a Hamilton cycle C=(x_1,...,x_n) in a graph G is k-symmetric, if the mapping x_i↦ x_i+n/k for all i=1,...,n, where indices are considered modulo n, is an automorphism of G.  ...  Note that the odd graph O k is the special Kneser graph K(2k + 1, k). Odd graphs O k , k ≥ 3, were shown to have a Hamilton cycle in [MNW21] , so κ(O k ) ≥ 1.  ... 
arXiv:2205.08126v1 fatcat:qcyqydytnrhhbmppozxgbzy3pm

On the central levels problem [article]

Petr Gregor, Ondřej Mička, Torsten Mütze
2021 arXiv   pre-print
., the vertices in the middle 2ℓ levels, has a Hamilton cycle for any m≥ 1 and 1≤ℓ≤ m+1.  ...  Our results also imply the existence of optimal cycles through any sequence of ℓ consecutive levels in the n-dimensional hypercube for any n≥ 1 and 1≤ℓ≤ n+1.  ...  The central levels problem studied in this paper is also closely related to another famous problem, which asks about Hamilton cycles in so-called bipartite Kneser graphs.  ... 
arXiv:1912.01566v2 fatcat:myrzkjm7grclnklxvhx3h2z6fm

A constant-time algorithm for middle levels Gray codes [article]

Torsten Mütze, Jerri Nummenpalo
2019 arXiv   pre-print
.,2n+1} such that any two consecutive subsets differ in adding or removing a single element.  ...  To appear in ACM Transactions on Algorithms, 2018] this existence proof was turned into an algorithm that computes each new set in the Gray code in time O(n) on average.  ...  Bipartite Kneser graphs are Hamiltonian. Combinatorica, 37(6):1207–1219, 2017. [MSW18] T. Mütze, C. Standke, and V. Wiechert.  ... 
arXiv:1606.06172v6 fatcat:25lf3f2sfzgzrox2uwfhpimeem

Minimal matrices in the Bruhat order for symmetric (0,1)-matrices

Henrique F. da Cruz, Rosário Fernandes, Susana Furtado
2017 Linear Algebra and its Applications  
The third type of talks were the 20-minute contributed talks running in two parallel sessions and given by 39 speakers.  ...  We have received 150 abstracts for 20-minute contributed talks which will run in four parallel sessions and cover a large variety of areas within graph theory and combinatorics.  ...  We show that, unlike for trees, all containments in the Venn diagram are proper for MOPs, a subfamily of 2-trees.  ... 
doi:10.1016/j.laa.2017.05.014 fatcat:zlcp5rb2sjeqvlyaajvf2nyoby

Automorphism Group and Other Properties of Zero Component Graph over a Vector Space

Shikun Ou, Yanqi Fan, Qunfang Li, Elena Guardo
2021 Journal of Mathematics  
In this paper, we introduce an undirected simple graph, called the zero component graph on finite-dimensional vector spaces.  ...  It is shown that two finite-dimensional vector spaces are isomorphic if and only if their zero component graphs are isomorphic, and any automorphism of a zero component graph can be uniquely decomposed  ...  In [14] , Boutin obtained sharp bounds for the fixing number of Kneser graphs and determined all Kneser graphs whose fixing number is 2, 3, or 4.  ... 
doi:10.1155/2021/5595620 fatcat:p6tjkpvjanaftp5kdgdywqnmku

On real number labelings and graph invertibility

Jeong-Ok Choi, John Georges, David Mauro, Yan Wang
2012 Discrete Applied Mathematics  
Acknowledgments The authors wish to thank the referees for their constructive comments that resulted in an improved paper.  ...  We have thus shown the following: Some examples of λ-invertible graphs In this section, we consider two families of graphs, the Kneser graphs and the line graphs of complete multipartite graphs, within  ...   (i) Kneser graphs and line graphs of complete graphs.  ... 
doi:10.1016/j.dam.2012.05.013 fatcat:46goumhis5ewnpe7gamhzuf4bm

Trimming and Gluing Gray Codes * †

Petr Gregor, Torsten Mütze
unpublished
Rephrased in terms of graph theory, our results establish the existence of (almost) Hamilton cycles in the subgraph of the n-dimensional cube Q n induced by all levels [k, l].  ...  . , k}, has a Hamilton cycle. We also prove an approximate version of this conjecture, showing that this graph has a cycle that visits a (1 − o(1))-fraction of all vertices.  ...  The authors thank Jiří Fink, Jerri Nummenpalo and Robert Šámal for several stimulating discussions about the problems discussed in this paper and the anonymous reviewers for their helpful comments.  ... 
fatcat:5ybpysrdejbk3nr3il52mazofu

Spanning connectedness and Hamiltonian thickness of graphs and interval graphs

Peng Li, Yaokun Wu
2015 Discrete Mathematics & Theoretical Computer Science  
International audience A spanning connectedness property is one which involves the robust existence of a spanning subgraph which is of some special form, say a Hamiltonian cycle in which a sequence of  ...  This paper suggests that much work in graph theory may have a spanning version which deserves further study, and that the Hamiltonian thickness may be a useful concept in understanding many spanning connectedness  ...  In §3. 2 For any graph G, Chvátal (23) found that t(G) ≥ κ(G) α(G) and equality holds when G is a complete bipartite graph.  ... 
doi:10.46298/dmtcs.2082 fatcat:jae2hlb3nbgybcf5t554uzjiq4
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