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A characterization for graphs having strong parity factors
[article]

2020
*
arXiv
*
pre-print

In this paper, we give

arXiv:2009.12802v1
fatcat:szf5ffva3fftbih354z562lwdq
*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. ...##
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On specific factors in graphs
[article]

2020
*
arXiv
*
pre-print

In this paper, we study this problem and generalize the concepts of even-

arXiv:1902.08689v2
fatcat:hjrcmyisyfc3pgqmbqlgoysrmi
*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. ...##
###
On Specific Factors in Graphs

2020
*
Graphs and Combinatorics
*

In this paper, we study this problem and generalize the concepts of even-

doi:10.1007/s00373-020-02225-1
fatcat:equiffldebbtlkij5jthycbr3i
*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. ...##
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Elementary Graphs with Respect to f-Parity Factors

2009
*
Graphs and Combinatorics
*

Then we use this reduction to investigate barriers and elementary

doi:10.1007/s00373-010-0878-0
fatcat:dt5bgtrboffeflg3ex7ee2c5zi
*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. ...##
###
A characterization of maximal non-k-factor-critical graphs

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. ...

##
###
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. ...##
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A Golden Ratio Parameterized Algorithm for Cluster Editing
[chapter]

2011
*
Lecture Notes in Computer Science
*

Finally, we use

doi:10.1007/978-3-642-25011-8_7
fatcat:kif6oj3r6bfenlkubucyvnrfoa
*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. ...##
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Charged pions tagged with polarized photons probing strong CP violation in a chiral-imbalance medium

2017
*
Physical Review C
*

Our findings might provide

doi:10.1103/physrevc.95.065204
fatcat:oq7z62bvijfzxdjjoorf67amwy
*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 ). ...##
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A golden ratio parameterized algorithm for Cluster Editing

2012
*
Journal of Discrete Algorithms
*

Third, we use

doi:10.1016/j.jda.2012.04.005
fatcat:2iy7cudorfbkpamhzysy6h2nau
*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. ...##
###
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, ...##
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Hanani-Tutte and Related Results
[chapter]

2013
*
Bolyai Society Mathematical Studies
*

In

doi:10.1007/978-3-642-41498-5_10
fatcat:tvikmzlc3bhvjijdnspdlhb4ey
*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. ...##
###
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

1998
*
Discrete Mathematics
*

Also

doi:10.1016/s0012-365x(97)00215-x
fatcat:6hpogomxe5fu5dzs2hduyt5mci
*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. ...##
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LDPC Decoding Techniques for Free-Space Optical Communications

2021
*
IEEE Access
*

In Fig. 3 an illustration of this

doi:10.1109/access.2021.3116081
fatcat:mwa3sjqjyffdxhcvcafy3zj574
*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*. ...##
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Finite State Markov Modeling of Fading Channels Towards Decoding of LDPC Codes
[article]

2019
*
arXiv
*
pre-print

We

arXiv:1912.09463v1
fatcat:r2lnjwip5bbnlabbp3u45ycvoa
*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). ...
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