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Cycles through subsets with large degree sums

1997
*
Discrete Mathematics
*

By 6(X) we denote the minimum

doi:10.1016/s0012-365x(96)00071-4
fatcat:o5vc5f4sibhibaagbrtdsv3fmm
*degree*(in G) of the vertices of X, and by a3(X) the minimum value of the*degree**sum*(in G) of any three pairwise nonadjacent vertices of X. ... We say that G is X-cyclable if G has an X-*cycle*, i.e., a*cycle*containing all vertices of X. ... Clearly x0 and the X-vertices xl ..... x~, of the proper 1-segments have*degree**sum*at least o'2+~(X). ...##
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An Optimized Algorithm for Constructing LDPC Code with Good Performance

고성능 LDPC 코드를 생성하기 위한 최적화된 알고리듬

2013
*
The Journal of the Korea institute of electronic communication sciences
*

고성능 LDPC 코드를 생성하기 위한 최적화된 알고리듬

In this paper, an algorithm having new edge growth

doi:10.13067/jkiecs.2013.8.8.1149
fatcat:xiuf6646wvcqbcrf54o6tpe2ee
*with*depth constraints for constructing Tanner graph of LDPC(Low density parity check) codes is proposed. ... To improve the performance, there are algo- algorithm [2] , this algorithm is*through*the heuristic search method, and constructing Tanner graphs*with**large*girth by establishing edges or connections ... That appearance in the worst case, the rest of the node in the*cycle**degree*is 2, at this time the ACE value of this*cycle*is 3, also greater than 2,*through*thus method, it can conform to the 6, 2 standard ...##
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Author index to volume 171 (1997)

1997
*
Discrete Mathematics
*

Veldman,

doi:10.1016/s0012-365x(97)89168-6
fatcat:i5igt5aqy5b63hto57s34i5cz4
*Cycles**through**subsets**with**large**degree**sums*(1 3) 43 54 Bryant, D.E., .A. Rodger and E.R. ... LieN, Euler*cycles*in the complete graph K2m+ 1 (1-3) 89 102 Egawa, Y., Contractible*cycles*in graphs*with**large*minimum*degree*(1--3) 103 119 Fon-Der-Flaass, D.G., Arrays of distinct representatives - ...##
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Structured LDPC codes for high-density recording: large girth and low error floor

2006
*
IEEE transactions on magnetics
*

However,

doi:10.1109/tmag.2005.861748
fatcat:bgbaqsw6u5fuxjjvijveq4jnky
*cycles*, especially short*cycles*, are harmful to LDPC codes. ... The paper describes the partition-and-shift LDPC (PS-LDPC) codes, a new class of regular, structured LDPC codes that can be designed*with**large*girth and arbitrary*large*minimum distance. ... To construct a regular LDPC code*with*uniform check node*degree*and bit node*degree*, we let each check node*subset*connect to bit node*subsets*and each bit node*subset*connect to check node*subsets*. ...##
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Cycles through particular subgraphs of claw-free graphs

1995
*
Journal of Graph Theory
*

This result is an analog of a result from the thesis of Fournier, and generalizes the result of Zhang that G is hamiltonian if the

doi:10.1002/jgt.3190200409
fatcat:ap5hk4ghpnf2nlmkdvhwtwgxke
*degree**sum*of any K(G) + 1 pairwise nonadjacent vertices is at least n ... We prove that G has a*cycle*containing all vertices of H whenever a 3 ( H ) 5 K(G), where a 3 ( H ) denotes the maximum number of vertices of H that are pairwise at distance at least three in G, and K( ... have "long"*cycles*containing particular sets of vertices*with*"*large*"*degree*. ...##
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Explicit Computation of Cheeger Constants for some Classes of Graphs

2019
*
Journal of Physics, Conference Series
*

More precisely, we deal

doi:10.1088/1742-6596/1127/1/012064
fatcat:vftmmpgcu5bpvmjzgvbhdusjwm
*with*the problem of splitting the graph into two*large*components of approximately equal volumes by making a small cut, which is the idea of Cheeger constant of a graph. ... We computed the Cheeger constants for simple classes of graphs such as 2-comb graphs,*cycle*graphs, complete graphs, and cube graphs. ... A*cycle*graph , sometimes simply known as an -*cycle*, is a graph on nodes containing a single*cycle**through*all nodes. In a*cycle*graph,*with*vertices, . ...##
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Below All Subsets for Some Permutational Counting Problems
[article]

2013
*
arXiv
*
pre-print

We show that the two problems of computing the permanent of an n× n matrix of poly(n)-bit integers and counting the number of Hamiltonian

arXiv:1211.0391v3
fatcat:frg4wqrrbfa7ncaa27gofbgcxm
*cycles*in a directed n-vertex multigraph*with*exp(poly(n)) edges ... We will*with*S 1 n denote the*subset*of S n of permutations consisting of exactly one such*cycle*. ... on n vertices, labeled 1*through*n,*with*the arcs i, σ(i) for all i. ...##
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On planar regular graphs degree three without Hamiltonian cycles
[article]

2009
*
arXiv
*
pre-print

Necessary condition to have Hamiltonian

arXiv:0908.2563v1
fatcat:s7evuozyrbgndc24xe3xwqmrgi
*cycle*in planar graph is given. Examples of regular planar graphs*degree*three without Hamiltonian*cycle*are built. ... Then, for any isobaric partition, first three faces should go into one*subset*of partition; border of partition would not go*through*x , and, as follows, Hamiltonian*cycle*would not be there. ... For the length of boundary*cycles*of faces ofG , there correspond*degrees*of vertices in ' G so that the task can be reduced to finding planar triangulations*with*arbitrary number of vertices of*degree*...##
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Cyclability and pancyclability in bipartite graphs

2001
*
Discrete Mathematics
*

Let S be a

doi:10.1016/s0012-365x(00)00425-8
fatcat:43eqgxxyfba4fhamxs37grxho4
*subset*of X of cardinality at least 3. We deÿne S to be cyclable in G if there exists a*cycle**through*all the vertices of S . ... We prove that if the*degree**sum*in G of every pair of nonadjacent vertices (x; y), x ∈ S, y ∈ Y is at least n + 1, then S is cyclable in G. ... In fact, the required condition can be lowered to the existence of an hamiltonian*cycle**with*two consecutive vertices having*degree**sum*greater or equal (or strictly greater if we do not accept exceptions ...##
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Scheduling Automated Traffic on a Network of Roads

2006
*
IEEE Transactions on Vehicular Technology
*

We present a polynomial time heuristic algorithm and evaluate its performance

doi:10.1109/tvt.2006.877472
fatcat:jsbbknjswbgldfxpma533dxde4
*through*simulations. ... We also address the optimization of performance*with*respect to delay, by focusing on the "one-step move" problem. ... The greedy-optimal algorithm uses essentially an exponentialtime brute force approach (*with*some slight refinements that reduce the exponent by a factor) at each time step, going*through*all possible*subsets*...##
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Page 6768 of Mathematical Reviews Vol. , Issue 98K
[page]

1998
*
Mathematical Reviews
*

. | David Burns (1-FERR; Big Rapids, MI)
98k:05098 05C38 05C35
Li, Jianping (PRC-YUN; Kunming)

*Cycles**through*many vertices of given*subsets*in |-tough graphs. (English and Chinese summaries) J. ... The minimum*degree**sum*among all essential independent sets of order 3 is denoted by a}(G). ...##
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A note on fundamental, non-fundamental, and robust cycle bases

2009
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Discrete Applied Mathematics
*

When analyzing such graphs, cyclically robust

doi:10.1016/j.dam.2008.06.047
fatcat:negpxc7jyfghlfw4wx4qqflz7e
*cycle*bases of are of interest since they can be used to generate all*cycles*of a given 2-connected graph by iteratively adding basis*cycles*. ... In many biological systems, robustness is achieved by redundant wiring, and reflected by the presence of*cycles*in the graphs connecting the systems' components. ... Each partial*sum*Q i of the*sum*-sequence generating C is a circuit. We finally conjecture that Hamilton graphs*with*vertex*degree*bounded by 3 have a cyclically robust*cycle*basis. ...##
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The Cycle Space of an Infinite Graph

2005
*
Combinatorics, probability & computing
*

*with*its ends. ... A notion of end

*degrees*motivated by these results opens up new possibilities for an 'extremal' branch of infinite graph theory. Numerous open problems are suggested. ... However, there is a way to introduce infinite

*sums*

*through*the back door: by using singular homology '

*with*cancellation'. ...

##
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Determinant Sums for Undirected Hamiltonicity
[article]

2010
*
arXiv
*
pre-print

We introduce the Labeled

arXiv:1008.0541v1
fatcat:xj4yqxyf7nbt3jwdc7u7oyqjo4
*Cycle*Cover*Sum*in which we are set to count weighted arc labeled*cycle*covers over a finite field of characteristic two. ... We reduce Hamiltonicity to Labeled*Cycle*Cover*Sum*and apply the determinant summation technique for Exact Set Covers (Björklund STACS 2010) to evaluate it. ... C∈cc(D) a∈C w(a). (3) We will see that Labeled*Cycle*Cover*Sum*can be evaluated*through*a*sum*of an exponential number of determinants. ...##
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Page 3453 of Mathematical Reviews Vol. , Issue 98F
[page]

1998
*
Mathematical Reviews
*

1-RI; Orsay);
Li, Jianping (PRC-YUN; Kunming);
Tian, Feng |Tian, Feng'| (PRC-ASBJ-S; Beijing);
Veldman, Henk Jan (NL-TWENA; Enschede)

*Cycles**through**subsets**with**large**degree**sums*. ... Rosa (3-MMAS; Hamilton, ON) 98f:05096 05C38 05C40 Egawa, Yoshimi (J-SUT-AM; Shinjuku) Contractible*cycles*in graphs*with**large*minimum*degree*. ...
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