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Rainbow Matchings of Size $\delta(G)$ in Properly Edge-Colored Graphs

2012
*
Electronic Journal of Combinatorics
*

Furthermore, we give an $O(\

doi:10.37236/2443
fatcat:mrcao4nhz5g6dftwb6rjwbruo4
*delta*(*G*)|V(*G*)|^2)$-time algorithm that generates such a matching in a properly edge-colored graph*of*order at least $6.5\*delta*$. ... Wang asked if there is a function $f(\*delta*)$ such that a properly edge-colored graph $*G*$ with minimum degree $\*delta*$ and order at least $f(\*delta*)$ must have a rainbow matching*of*size $\*delta*$. ... Thus,*for*small values*of*i,*the**bound*c i ≤ 2(k − i + 1) can likely be*improved*. However, we doubt that such analysis*of*this algorithm can be*improved*to yield a*bound*on |V (*G*)| better than 6δ. ...##
###
Nucleon to delta electromagnetic transition in the Dyson-Schwinger approach

2012
*
Physical Review D
*

*The*nucleon and

*Delta*baryons are treated as quark-diquark

*bound*states, where

*the*ingredients

*of*

*the*electromagnetic transition current are computed self-consistently from

*the*underlying dynamics in QCD ... This implies that

*the*deformation from a spherical charge distribution inside both baryons can be traced back to

*the*appearance

*of*p waves in

*the*nucleon and

*Delta*

*bound*-state amplitudes which are a consequence ...

*The*nucleon and ∆ deformation is tightly

*connected*to

*the*understanding

*of*their internal structure. ...

##
###
Delta and omega electromagnetic form factors in a Dyson-Schwinger/Bethe-Salpeter approach

2010
*
Physical Review D
*

We use a consistent setup

doi:10.1103/physrevd.82.114017
fatcat:qurma4ffqrbx5p7iw7j72k6t54
*for**the*quark-gluon dressing,*the*quark-quark*bound*-state kernel and*the*quark-photon interaction. ... We investigate*the*electromagnetic form factors*of**the**Delta*and*the*Omega baryons within*the*Poincare-covariant framework*of*Dyson-Schwinger and Bethe-Salpeter equations. ...*The**lower*left diagram is*the*respective coupling to*the*diquark and depends on*the*axial-vector diquark-photon*vertex*. ...##
###
D-state effects in the electromagneticNΔtransition

2008
*
Physical Review D
*

By parametrizing

doi:10.1103/physrevd.78.114017
fatcat:vkm6cev5xzfd7i35rjhdtoebma
*the*pion cloud contribution*for**the*transition electric and Coulomb form factors in terms*of**the*neutron electric form factor, we estimate that*the*contributions*of**the**Delta*D-state coupled ... to quark core spin*of*3/2 is*of**the*order*of*1%, and*the*contributions*of**the**Delta*D-state coupled to quark core spin 1/2 is*of**the*order*of*4%. ... Acknowledgments*G*. R. wants to thank Vadim Guzey, José Goity and Kazuo Tsushima*for**the*helpful discussions.*The*authors want also to thank to B. Juliá Díaz*for*sharing*the*'bare data'*of*Ref. ...##
###
The muon $g$-2 and $\Delta \alpha$ connection

2020
*
The muon $g$-2 and $\Delta \alpha$ connection
*
unpublished

Size

doi:10.2172/1668375
fatcat:g3oop6323zg4theeccbqqyfdmu
*of*missed contributions would need to be implausibly large given*the*robust status*of**the*hadronic cross section measurements. 08/24/20 Alex Keshavarzi |*The*muon*g*-2 and Δ*connection*Keshavarzi, ... How realistic are*the*required shifts in σ(s)? ... Aiming*for*x4*improvement*in total uncertainty. Analysis*of*Run-1 data being finalised*for*publication. → Will confirm validity*of*Muon*g*-2 discrepancy and potential*for*BSM discovery. ...##
###
Improved Guarantees for Vertex Sparsification in Planar Graphs
[article]

2017
*
arXiv
*
pre-print

It

arXiv:1702.01136v1
fatcat:pghxyimrvfgptl7vgq5ubynyai
*improves**the*previous best-known*bound**of*O(k^22^2k)*for*cut and flow sparsifiers by an exponential factor, and matches an Ω(k^2)*lower*-*bound**for*this class*of*graphs. ... We show any directed graph*G*admits a RPM H*of*size O(k^3), and if*G*is planar, then*the*size*of*H*improves*to O(k^2 k). ... Khan and Raghavendra [22] gave an*improved*upper*bound*(while still doubly exponential in k)*for*general graphs as well as a*lower**bound**of*2 (k−1)/2*for*general graphs. ...##
###
Estimating the number of disjoint edges in simple topological graphs via cylindrical drawings
[article]

2013
*
arXiv
*
pre-print

By combining our result with a result

arXiv:1307.4191v1
fatcat:jwqtwtxi3bhl3bmbd25bbqd32q
*of*T\'oth we obtain an alternative proof*for**the*best known*lower**bound**of*$\Omega(n^\frac 13)$ on*the*maximum number*of*pairwise disjoint edges in a simple complete ... We show that*for*every simple complete topological graph $*G*$ there exists $\*Delta*$, $0<\*Delta*<n$, such that $*G*$ contains at least $\max \{\frac n\*Delta*, c(\*Delta*)\}$ pairwise disjoint edges. ... Note that any*improvement**of*this*lower**bound*would translate into a better*bound*in Theorem 1.2. ...##
###
Bisected vertex leveling of plane graphs: braid index, arc index and delta diagrams
[article]

2018
*
arXiv
*
pre-print

We also find a quadratic upper

arXiv:1806.09719v1
fatcat:4hfvq6c4v5gpja7zat5py7xxca
*bound**of**the*minimal crossing number*of**delta*diagrams*of*L. ... Using this planar embedding, we present elementary proofs*of**the*well-known upper*bounds*in terms*of**the*minimal crossing number on braid index b(L) and arc index α(L)*for*any knot or non-split link L, ...*The*component D 1 contains another candidate*vertex*w 2 ;*for*otherwise, w 1 is a cut*vertex**of**G*. Suppose further that*the*part*of**G*\{w 2 } lying above y = k is not*connected*. ...##
###
The Delta-Wye Approximation Procedure for Two-Terminal Reliability

1996
*
Operations Research
*

It combines

doi:10.1287/opre.44.5.745
fatcat:2cux534wifgabhtsfsnuwghyqi
*the*probability equations*of*Lehman | whose solutions provide*bounds*and approximations*of*twoterminal reliability*for**the*individual transformations | with*the**Delta*-Wye Reduction Algorithm ...*The**Delta*-Wye Approximation Procedure (DWAP) is a procedure*for*estimating*the*two-terminal reliability*of*an undirected planar network*G*= (V; E) by reducing*the*network to a single edge via a sequence ... vectors p l , p u and p ,*for*which*the*value*of*R(*G*; p) at each*of*these three vectors is a*lower**bound*, upper*bound*and best estimate*for*R(*G*0 ; p 0 ); respectively. ...##
###
A Strengthening of Brooks' Theorem for Line Graphs

2011
*
Electronic Journal of Combinatorics
*

We prove that if $

doi:10.37236/632
fatcat:a7vfs42gijaalagu2kayejaira
*G*$ is*the*line graph*of*a multigraph, then*the*chromatic number $\chi(*G*)$*of*$*G*$ is at most $\max\left\{\omega(*G*), \frac{7\*Delta*(*G*) + 10}{8}\right\}$ where $\omega(*G*)$ and $\*Delta*(*G*)$ ... Thus*the*Borodin-Kostochka Conjecture holds*for*line graphs*of*multigraphs. ... Acknowledgments Thanks to anonymous referee*for*helping to*improve**the*readability*of**the*paper. ...##
###
Lazy Constraint Imposing for Improving the Path Constraint

2009
*
Electronical Notes in Theoretical Computer Science
*

In this paper we propose a lazy constraint imposing mechanism

doi:10.1016/j.entcs.2009.10.020
fatcat:dpfghkb7tzaedkjpnisvpcl6ga
*for**improving**the*path constraint in GRASPER, a state-*of*-*the*-art graph constraint solver, having obtained very promising results in terms*of*... both time and space in solving an interesting problem in*the*Biochemistry subject area, in comparison with CP(Graph),*the*state-*of*-*the*-art solver. ... Such*bounds*are denoted as glb (greatest*lower**bound*) and lub (least upper*bound*). ...##
###
Transitive Tournament Tilings in Oriented Graphs with Large Minimum Total Degree

2021
*
SIAM Journal on Discrete Mathematics
*

We thank

doi:10.1137/19m1269257
fatcat:7r6r667tlfdo7d7mgp5z7vmwt4
*the*organizers*of*this conference*for**the*stimulating work environment. We also thank*the*referees*for*their helpful and careful reviews. ... This project began during*the*``Recent Advances in Extremal Combinatorics Workshop"" at*the*Tsinghua Sanya International Mathematics Forum, May 22--26, 2017. ... Therefore, it is possible that a substantial*improvement*to*the*upper*bound*on \vec{} tr \ast (k) could give an*improvement*on*the*best known*lower**bound**for**the*diagonal Ramsey numbers. ...##
###
$\delta$-Connectivity in Random Lifts of Graphs

2017
*
Electronic Journal of Combinatorics
*

We also simplify a later result showing a

doi:10.37236/6639
fatcat:idf6pjwcfjhljgybgly4xmoyxu
*lower**bound*on*the*edge expansion*of*random lifts. ...*the*case*for*subgroups*of**the*symmetric group. ... Scholarship*for*Research. ...##
###
Strengthened Brooks' Theorem for Digraphs of Girth at least Three

2011
*
Electronic Journal of Combinatorics
*

A result

doi:10.37236/682
fatcat:oiusc4lzibbvlomjcwxpusg2rq
*of*Johansson shows that if $*G*$ is triangle-free, then*the*chromatic number drops to $O(\*Delta*/ \log \*Delta*)$. In this paper, we derive a weak analog*for**the*chromatic number*of*digraphs. ... Brooks' Theorem states that a*connected*graph $*G*$*of*maximum degree $\*Delta*$ has chromatic number at most $\*Delta*$, unless $*G*$ is an odd cycle or a complete graph. ... This will give us a*lower**bound*on E[X v ]. There are C choices*for*color i and at least c 1∆ 2 choices*for**the*set {u, w}. ...##
###
Sharper Lower Bounds in the Maximum Degree and Diameter Bounded Subgraph Problem in the Mesh
[article]

2012
*
arXiv
*
pre-print

We provide

arXiv:1211.7128v1
fatcat:i2p3qbk7znathkeutjdq2yus5a
*lower**bounds**for**the*size*of**the*largest subgraph*of**the*mesh satisfying MaxDDBS*for*all k and \*Delta*> 3 that agree with*the*known upper*bounds*up to*the*first two terms, and show that*for*... \*Delta*= 3,*the**lower**bounds*are at least*the*same order*of*growth as*the*upper*bounds*. ... I would like to thank to Joe Gallian, and*the*advisors, Adam Hesterberg, Eric Riedl, and Davie Rolnick*for*all*of*their help. ...
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