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A characterization for graphs having strong parity factors [article]

Hongliang Lu, Zixuan Yang, Xuechun Zhang
2020 arXiv   pre-print
In this paper, we give a characterization for graphs to have the strong parity property and construct a counterexample to disprove the conjecture proposed by Bujtás, Jendrol and Tuza.  ...  A graph G has the strong parity property if for every subset X⊆ V with |X| even, G has a spanning subgraph F with minimum degree at least one such that d_F(v)≡ 1 2 for all v∈ X, d_F(y)≡ 0 2 for all y∈  ...  Every 2-edge-connected graph of minimum degree at least three has the strong parity property. In this paper, we give a characterization for a graph to have a strong parity factor. Theorem 2.  ... 
arXiv:2009.12802v1 fatcat:szf5ffva3fftbih354z562lwdq

On specific factors in graphs [article]

Csilla Bujtás, Stanislav Jendrol, Zsolt Tuza
2020 arXiv   pre-print
In this paper, we study this problem and generalize the concepts of even-factors and odd-factors in a unified form.  ...  have an even degree in H.  ...  The authors would like to thank Július Czap for his helpful comments.  ... 
arXiv:1902.08689v2 fatcat:hjrcmyisyfc3pgqmbqlgoysrmi

On Specific Factors in Graphs

Csilla Bujtás, Stanislav Jendrol', Zsolt Tuza
2020 Graphs and Combinatorics  
In this paper, we study this problem and generalize the concepts of even-factors and odd-factors in a unified form. ().,-volV) (0123456789().,-volV)  ...  vertices have an even degree in H.  ...  as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.  ... 
doi:10.1007/s00373-020-02225-1 fatcat:equiffldebbtlkij5jthycbr3i

Elementary Graphs with Respect to f-Parity Factors

Mikio Kano, Gyula Y. Katona, Jácint Szabó
2009 Graphs and Combinatorics  
Then we use this reduction to investigate barriers and elementary graphs with respect to f -parity factors, where an elementary graph is a graph such that the union of f -parity factors form a connected  ...  This note concerns the f -parity subgraph problem, i.e., we are given an undirected graph G and a positive integer value function f : V (G) → N, and our goal is to find a spanning subgraph F of G with  ...  The (1, f)-odd subgraph problem was first investigated by Amahashi [1] , who gave a Tutte type characterization of graphs having a [1, n]-odd factor, where n ≥ 1 is an odd integer.  ... 
doi:10.1007/s00373-010-0878-0 fatcat:dt5bgtrboffeflg3ex7ee2c5zi

A characterization of maximal non-k-factor-critical graphs

N. Ananchuen, L. Caccetta, W. Ananchuen
2007 Discrete Mathematics  
A graph G of order p is k-factor-critical,where p and k are positive integers with the same parity, if the deletion of any set of k vertices results in a graph with a perfect matching.  ...  A complete characterization of maximal non-k-factor-critical graphs, maximal non-k-extendable graphs and maximal non-k-extendable bipartite graphs is given.  ...  Let G be a connected graph on p vertices and k a positive integer having the same parity with p.  ... 
doi:10.1016/j.disc.2006.05.036 fatcat:fnkdv7htozabhofhp52yxh6ioq

Page 2763 of Mathematical Reviews Vol. , Issue 98E [page]

1998 Mathematical Reviews  
In the present paper the authors show that a graph G has a strong S,-factor (nm > 2) if and only if oc(G — S) < n\S| for all subsets S Cc V(G).  ...  of G, is called a strong S,-factor of G.  ... 

A Golden Ratio Parameterized Algorithm for Cluster Editing [chapter]

Sebastian Böcker
2011 Lecture Notes in Computer Science  
Finally, we use a known characterization of graphs with few conflicts. This is a preprint of: Sebastian Böcker. A golden ratio parameterized algorithm for Cluster Editing.  ...  We present a novel search tree algorithm for the problem, which improves running time from O * (1.76 k ) to O * (1.62 k ).  ...  First, we consider the case of three strong conflict triples: Lemma 2. Let G be an integer-weighted graph that has the parity property.  ... 
doi:10.1007/978-3-642-25011-8_7 fatcat:kif6oj3r6bfenlkubucyvnrfoa

Charged pions tagged with polarized photons probing strong CP violation in a chiral-imbalance medium

Mamiya Kawaguchi, Masayasu Harada, Shinya Matsuzaki, Ruiwen Ouyang
2017 Physical Review C  
Our findings might provide a novel possibility to make a manifest detection for the remnant of the strong CP violation.  ...  Heavy ion collision experiments could observe the phenomenological consequence of this parity-odd form factor through the elastic scattering of a pion and a photon in the medium.  ...  (6) , just for later convenience, we have defined the form factor F 1 by extracting the factor (p 0 + p ′0 ).  ... 
doi:10.1103/physrevc.95.065204 fatcat:oq7z62bvijfzxdjjoorf67amwy

A golden ratio parameterized algorithm for Cluster Editing

Sebastian Böcker
2012 Journal of Discrete Algorithms  
Third, we use a known characterization of graphs with few conflicts.  ...  We then show that Integer-Weighted Cluster Editing remains NP-hard for graphs that have a particularly simple structure: namely, a clique minus the edges of a triangle.  ...  Acknowledgement I would like to thank François Nicolas for helpful discussions.  ... 
doi:10.1016/j.jda.2012.04.005 fatcat:2iy7cudorfbkpamhzysy6h2nau

Page 2465 of Mathematical Reviews Vol. , Issue 94e [page]

1994 Mathematical Reviews  
number equals 28* or 28* +1 (depending on parity), where 8* denotes the strong matching num- ber.  ...  In this paper we give a necessary and sufficient condition for K,,,, to have a P>)-factorization.” 94e:05199 05C70 05C05 Wang, Hong [Wang, Hong’ (3-CALG; Calgary, AB); Sauer, Norbert (3-CALG; Calgary,  ... 

Hanani-Tutte and Related Results [chapter]

Marcus Schaefer
2013 Bolyai Society Mathematical Studies  
In a recent paper [34] we introduced the name "strong Hanani-Tutte theorem" to distinguish it from a weaker version that is also often called the Hanani-Tutte theorem in the literature.  ...  other oddly. 1 Since by Kuratowski's theorem every non-planar graph contains a subdivision of K 5 or K 3,3 , Hanani's observation implies that any drawing of a nonplanar graph contains two vertex-disjoint  ...  Without them there would have been less to survey.  ... 
doi:10.1007/978-3-642-41498-5_10 fatcat:tvikmzlc3bhvjijdnspdlhb4ey

Page 65 of Mathematical Reviews Vol. , Issue 2001A [page]

2001 Mathematical Reviews  
Summary: “A graph G of order n is p-factor-critical, where p is an integer of the same parity as n, if the removal of any set of p vertices of G results in a graph with a perfect matching.  ...  We show that for p even, every non-bipartite p-extendable graph is p-factor-critical, and every non-bipartite (p + 1)-extendable graph G is such that G —e is p-factor-critical for every edge e of G.  ... 

Hamilton cycles in tensor product of graphs

R. Balakrishnan, P. Paulraja
1998 Discrete Mathematics  
Also a characterization for a 4-regular graph to have a bieulerian orientation is presented.  ...  In this paper, we characterize graphs G for which G®K2 is Hamiltonian, where ® denotes the tensor product of graphs.  ...  Bermond for their kind hospitality during their visit.  ... 
doi:10.1016/s0012-365x(97)00215-x fatcat:6hpogomxe5fu5dzs2hduyt5mci

LDPC Decoding Techniques for Free-Space Optical Communications

Albashir A. Youssef, Mohamed Abaza, Ayshah S. Alatawi
2021 IEEE Access  
In Fig. 3 an illustration of this graph for a certain code is shown. Fig. 3 shows Tanner A.  ...  Many channels mathematical models have been proposed to identify turbulence from strong-to-weak regimes. These models have probability density functions (pdf) and are illustrated below. A.  ... 
doi:10.1109/access.2021.3116081 fatcat:mwa3sjqjyffdxhcvcafy3zj574

Finite State Markov Modeling of Fading Channels Towards Decoding of LDPC Codes [article]

Mohit Kumar
2019 arXiv   pre-print
We have gone for a two-state system as it shows a good compromise between complexity and performance.  ...  Here we have proposed two decoding strategies of low-density parity-check (LDPC) codes over Markov noise channels with bit flipping noise.  ...  Here, let the decoding procedure be if both the parity check fails for a digit, then change the digit (because of the strong indication of error of the digit as both parity checks have failed).  ... 
arXiv:1912.09463v1 fatcat:r2lnjwip5bbnlabbp3u45ycvoa
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