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Cycles through subsets with large degree sums

Hajo Broersma, Hao Li, Jianping Li, Feng Tian, Henk Jan Veldman
1997 Discrete Mathematics  
By 6(X) we denote the minimum 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).  ... 
doi:10.1016/s0012-365x(96)00071-4 fatcat:o5vc5f4sibhibaagbrtdsv3fmm

An Optimized Algorithm for Constructing LDPC Code with Good Performance
고성능 LDPC 코드를 생성하기 위한 최적화된 알고리듬

Hee-Jong Suh
2013 The Journal of the Korea institute of electronic communication sciences  
In this paper, an algorithm having new edge growth 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  ... 
doi:10.13067/jkiecs.2013.8.8.1149 fatcat:xiuf6646wvcqbcrf54o6tpe2ee

Author index to volume 171 (1997)

1997 Discrete Mathematics  
Veldman, 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 -  ... 
doi:10.1016/s0012-365x(97)89168-6 fatcat:i5igt5aqy5b63hto57s34i5cz4

Structured LDPC codes for high-density recording: large girth and low error floor

J. Lu, J.M.F. Moura
2006 IEEE transactions on magnetics  
However, 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.  ... 
doi:10.1109/tmag.2005.861748 fatcat:bgbaqsw6u5fuxjjvijveq4jnky

Cycles through particular subgraphs of claw-free graphs

H. J. Broersma, M. Lu
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 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.  ... 
doi:10.1002/jgt.3190200409 fatcat:ap5hk4ghpnf2nlmkdvhwtwgxke

Explicit Computation of Cheeger Constants for some Classes of Graphs

S Opiyo, Y Soeharyadi, M W Setyabudhi
2019 Journal of Physics, Conference Series  
More precisely, we deal 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, .  ... 
doi:10.1088/1742-6596/1127/1/012064 fatcat:vftmmpgcu5bpvmjzgvbhdusjwm

Below All Subsets for Some Permutational Counting Problems [article]

Andreas Björklund
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 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.  ... 
arXiv:1211.0391v3 fatcat:frg4wqrrbfa7ncaa27gofbgcxm

On planar regular graphs degree three without Hamiltonian cycles [article]

Emanuels Grinbergs
2009 arXiv   pre-print
Necessary condition to have Hamiltonian 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  ... 
arXiv:0908.2563v1 fatcat:s7evuozyrbgndc24xe3xwqmrgi

Cyclability and pancyclability in bipartite graphs

Mohamed El Kadi Abderrezzak, Evelyne Flandrin, Denise Amar
2001 Discrete Mathematics  
Let S be a 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  ... 
doi:10.1016/s0012-365x(00)00425-8 fatcat:43eqgxxyfba4fhamxs37grxho4

Scheduling Automated Traffic on a Network of Roads

A. Giridhar, P.R. Kumar
2006 IEEE Transactions on Vehicular Technology  
We present a polynomial time heuristic algorithm and evaluate its performance 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  ... 
doi:10.1109/tvt.2006.877472 fatcat:jsbbknjswbgldfxpma533dxde4

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).  ... 

A note on fundamental, non-fundamental, and robust cycle bases

Konstantin Klemm, Peter F. Stadler
2009 Discrete Applied Mathematics  
When analyzing such graphs, cyclically robust 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.  ... 
doi:10.1016/j.dam.2008.06.047 fatcat:negpxc7jyfghlfw4wx4qqflz7e

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'.  ... 
doi:10.1017/s0963548304006686 fatcat:kuyz7n4oaje7nebydwjkmu6l3e

Determinant Sums for Undirected Hamiltonicity [article]

Andreas Björklund
2010 arXiv   pre-print
We introduce the Labeled 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.  ... 
arXiv:1008.0541v1 fatcat:xj4yqxyf7nbt3jwdc7u7oyqjo4

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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