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

Jennifer Diemunsch, Michael Ferrara, Allan Lo, Casey Moffatt, Florian Pfender, Paul S Wenger
2012 Electronic Journal of Combinatorics  
Furthermore, we give an $O(\delta(G)|V(G)|^2)$-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.  ... 
doi:10.37236/2443 fatcat:mrcao4nhz5g6dftwb6rjwbruo4

Nucleon to delta electromagnetic transition in the Dyson-Schwinger approach

G. Eichmann, D. Nicmorus
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.  ... 
doi:10.1103/physrevd.85.093004 fatcat:rufwevj3gfapzjlabpdpke43aq

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

D. Nicmorus, G. Eichmann, R. Alkofer
2010 Physical Review D  
We use a consistent setup 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.  ... 
doi:10.1103/physrevd.82.114017 fatcat:qurma4ffqrbx5p7iw7j72k6t54

D-state effects in the electromagneticNΔtransition

G. Ramalho, M. T. Peña, Franz Gross
2008 Physical Review D  
By parametrizing 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.  ... 
doi:10.1103/physrevd.78.114017 fatcat:vkm6cev5xzfd7i35rjhdtoebma

The muon $g$-2 and $\Delta \alpha$ connection

Alex Keshavarzi
2020 The muon $g$-2 and $\Delta \alpha$ connection   unpublished
Size 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.  ... 
doi:10.2172/1668375 fatcat:g3oop6323zg4theeccbqqyfdmu

Improved Guarantees for Vertex Sparsification in Planar Graphs [article]

Gramoz Goranci, Monika Henzinger, Pan Peng
2017 arXiv   pre-print
It 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.  ... 
arXiv:1702.01136v1 fatcat:pghxyimrvfgptl7vgq5ubynyai

Estimating the number of disjoint edges in simple topological graphs via cylindrical drawings [article]

Radoslav Fulek
2013 arXiv   pre-print
By combining our result with a result 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.  ... 
arXiv:1307.4191v1 fatcat:jwqtwtxi3bhl3bmbd25bbqd32q

Bisected vertex leveling of plane graphs: braid index, arc index and delta diagrams [article]

Sungjong No, Seungsang Oh, Hyungkee Yoo
2018 arXiv   pre-print
We also find a quadratic upper 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.  ... 
arXiv:1806.09719v1 fatcat:4hfvq6c4v5gpja7zat5py7xxca

The Delta-Wye Approximation Procedure for Two-Terminal Reliability

Manoj K. Chari, Thomas A. Feo, J. Scott Provan
1996 Operations Research  
It combines 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.  ... 
doi:10.1287/opre.44.5.745 fatcat:2cux534wifgabhtsfsnuwghyqi

A Strengthening of Brooks' Theorem for Line Graphs

Landon Rabern
2011 Electronic Journal of Combinatorics  
We prove that if $G$ 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.  ... 
doi:10.37236/632 fatcat:a7vfs42gijaalagu2kayejaira

Lazy Constraint Imposing for Improving the Path Constraint

Ruben Duarte Viegas, Francisco Azevedo
2009 Electronical Notes in Theoretical Computer Science  
In this paper we propose a lazy constraint imposing mechanism 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).  ... 
doi:10.1016/j.entcs.2009.10.020 fatcat:dpfghkb7tzaedkjpnisvpcl6ga

Transitive Tournament Tilings in Oriented Graphs with Large Minimum Total Degree

Louis DeBiasio, Allan Lo, Theodore Molla, Andrew Treglown
2021 SIAM Journal on Discrete Mathematics  
We thank 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.  ... 
doi:10.1137/19m1269257 fatcat:7r6r667tlfdo7d7mgp5z7vmwt4

$\delta$-Connectivity in Random Lifts of Graphs

Shashwat Silas
2017 Electronic Journal of Combinatorics  
We also simplify a later result showing a lower bound on the edge expansion of random lifts.  ...  the case for subgroups of the symmetric group.  ...  Scholarship for Research.  ... 
doi:10.37236/6639 fatcat:idf6pjwcfjhljgybgly4xmoyxu

Strengthened Brooks' Theorem for Digraphs of Girth at least Three

Ararat Harutyunyan, Bojan Mohar
2011 Electronic Journal of Combinatorics  
A result 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}.  ... 
doi:10.37236/682 fatcat:oiusc4lzibbvlomjcwxpusg2rq

Sharper Lower Bounds in the Maximum Degree and Diameter Bounded Subgraph Problem in the Mesh [article]

Sachi Hashimoto
2012 arXiv   pre-print
We provide 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.  ... 
arXiv:1211.7128v1 fatcat:i2p3qbk7znathkeutjdq2yus5a
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