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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. ...##
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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*...##
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Combinatorial Gray codes-an updated survey
[article]

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

arXiv:2202.01280v1
fatcat:dnjvd2zih5dxrgs3vrwsfyhafi
*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*. ...##
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Problems in Algebraic Combinatorics

1995
*
Electronic Journal of Combinatorics
*

This is a list of open problems, mainly

doi:10.37236/1224
fatcat:etalsageu5awhdkehlcmt3uln4
*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] . ...##
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Graphs as navigational infrastructure for high dimensional data spaces

2011
*
Computational statistics (Zeitschrift)
*

These are connected to known results

doi:10.1007/s00180-011-0228-6
fatcat:v6wmxh3vq5agpfw3widxpd7yji
*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). ...##
###
Master index of volumes 71–80

1990
*
Discrete Mathematics
*

Quintana,

doi:10.1016/0012-365x(90)90304-z
fatcat:tp4gu4hk2fbrdawvvu4vcsupii
*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. ...##
###
Trimming and gluing Gray codes

2018
*
Theoretical Computer Science
*

Rephrased

doi:10.1016/j.tcs.2017.12.003
fatcat:rgdurlmhy5aqlfpzsuw3m5jf4u
*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. ...##
###
The Hamilton compression of highly symmetric graphs
[article]

2022
*
arXiv
*
pre-print

We refer to the maximum k for which there exists a k-symmetric

arXiv:2205.08126v1
fatcat:qcyqydytnrhhbmppozxgbzy3pm
*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. ...##
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On the central levels problem
[article]

2021
*
arXiv
*
pre-print

., the vertices

arXiv:1912.01566v2
fatcat:myrzkjm7grclnklxvhx3h2z6fm
*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*. ...##
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A constant-time algorithm for middle levels Gray codes
[article]

2019
*
arXiv
*
pre-print

.,2n+1} such that any

arXiv:1606.06172v6
fatcat:25lf3f2sfzgzrox2uwfhpimeem
*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. ...##
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Minimal matrices in the Bruhat order for symmetric (0,1)-matrices

2017
*
Linear Algebra and its Applications
*

The third type of talks were the 20-minute contributed talks running

doi:10.1016/j.laa.2017.05.014
fatcat:zlcp5rb2sjeqvlyaajvf2nyoby
*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. ...##
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Automorphism Group and Other Properties of Zero Component Graph over a Vector Space

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. ...

##
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On real number labelings and graph invertibility

2012
*
Discrete Applied Mathematics
*

Acknowledgments The authors wish to thank the referees for their constructive comments that resulted

doi:10.1016/j.dam.2012.05.013
fatcat:46goumhis5ewnpe7gamhzuf4bm
*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*. ...##
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Trimming and Gluing Gray Codes * †

unpublished

Rephrased

fatcat:5ybpysrdejbk3nr3il52mazofu
*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. ...##
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Spanning connectedness and Hamiltonian thickness of graphs and interval graphs

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

doi:10.46298/dmtcs.2082
fatcat:jae2hlb3nbgybcf5t554uzjiq4
*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*. ...
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