A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Filters
Net structure and cages
1979
Discrete Mathematics
Preserved Fulltext
An embeddable g net of valency k corresponds to a graph of girth g which can be drawn on a surface in such a way that every face is bounded by a circuit of length g. ...
A g cage of valency k is a regu' -bU. graph of girth g and valency k with the minimum number of vertices consistent with this conciition [12]. ...
The former for discussions on residual finiteness resulting in the proof of Theorem 11 and the latter for supervising him during the period when the major part of this work was produced. ...
doi:10.1016/0012-365x(79)90110-9
fatcat:34i5bbwsxvelfohb7gfk5t62pq
Isomorphism of graphs of bounded valence can be tested in polynomial time
1982
Journal of computer and system sciences (Print)
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
It is shown that testing isomorphism of graphs of bounded valance is polynomial-time reducible to the color automorphism problem for groups with composition factors of bounded order. ...
In the trivalent case p = 2, P = G and the analysis requires only elementary notions. For higher valence, the justification requires some new observations about primitive permutation groups. ...
THE BOUNDED VALENCE CASE
The Groups That Arise We now consider graphs of valence <t where t is, henceforth, fixed. ...
doi:10.1016/0022-0000(82)90009-5
fatcat:dwxhyw4o7ng33owfqwnu7rayoa
On the graph labellings arising from phylogenetics
2013
Open Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Our main theorem bounds the degree of the generators of the semigroup by g + 1 when the graph has first Betti number g. Also, we provide a series of examples where the bound is sharp. ...
AbstractWe study semigroups of labellings associated to a graph. ...
The authors would like to thank Christian Haase and Andreas Paffenholz for helpful discussions, Alexander Kasprzyk and Zach Teitler for their comments that have helped to improve the presentation. ...
doi:10.2478/s11533-013-0263-3
fatcat:arsdk6s5obc4lnjksrsu7zmnza
Graph curves
1991
Advances in Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
For any set A of vertices of a graph G of valency 1, define a retraction operator rA by rA(G) = G-A. If A is the set of vertices of valency 1, then we will write r(G) for rA(G). ...
Bayer and D. Eisenbud introduce the combinatorial Clifford index for trivalent graphs and prove that this is the same as the resolution Clifford index for plane trivalent graphs. ...
For the same reason, {cl, c,_~} is the set of vertices of G3, each of which is incident to one of the pairs of vertices {u,, uz} and {u,-,, u,}. We may assume that ci is incident to vr. ...
doi:10.1016/0001-8708(91)90034-5
fatcat:f3divaxzdnhrhmy3fkt4xhq2xy
Page 2754 of Mathematical Reviews Vol. , Issue 2004d
[page]
2004
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
The author defines three special families of metacir- culant graphs of valency 4 and then shows that any non-Cayley metacirculant graph of valency 4 is isomorphic to a union of disjoint copies of a graph ...
As corollaries, asymptotics of the form cj(n) ~ ajn ge (called the normal rate) as n — oo are derived for the corresponding numbers of maps c;(”), where x; satisfies an algebraic equation of degree 6, ...
Small vertex-transitive graphs of given degree and girth
2011
Ars Mathematica Contemporanea
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
We prove the existence of k-valent Cayley graphs of girth g for every pair of parameters k ≥ 2 and g ≥ 3, improve the lower bounds on the order of the smallest (k, g) vertex-transitive graphs for certain ...
Small vertex-transitive graphs of given degree and girth. Ars Mathematica Contemporanea, 4(2) pp. 375-384. For guidance on citations see FAQs. ...
For every pair of parameters k ≥ 2, g ≥ 3, there exists a finite Cayley graph C(Γ, X) of valence k and girth g.
Proof. ...
doi:10.26493/1855-3974.124.06d
fatcat:u57sdizqh5fsvexqkqys4zog6e
Foreword
2009
Journal of Mathematical Sciences
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
However, as soon as we change the abstract graphs for the ribbon graphs or, equivalently, fix an embedding of a graph into an oriented surface, we find that such an object represents a complicated arithmetic ...
The first publication where some of the constructions of the Esquisse were represented in the traditional mathematical form was the paper of 1990 by G. Shabat and V. ...
Artamkin's paper gives a beautiful, nontrivial, and self-contained description of the 2-faced dessins with trivalent graphs. ...
doi:10.1007/s10958-009-9367-5
fatcat:mztvsoitujgqbfjrrrbv3pkeqy
Invariants of theta-curves and other graphs in 3-space
1993
Topology and its Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2012; you can also visit the original URL.
The file type is application/pdf.
It turns out that &curves and &-graphs are the unique graphs for which this approach works. ...
We consider, in particular, surfaces that contain the graph as a spine and that are canonical in the sense of having trivial Seifert linking form. ...
Acknowledgement We thank the referee for an excellent job proofreading the manuscript, for correcting an error in a link polynomial computation, and for supplying us with a computation that provides an ...
doi:10.1016/0166-8641(93)90110-y
fatcat:srswnzeoxbdpze3lps2ci5cklq
Page 5294 of Mathematical Reviews Vol. , Issue 93j
[page]
1993
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
Summary: “Leland and Solomon introduced a family of trivalent graphs, called Mobius graphs, and because of their small diameter suggested that they be used as an effective interconnection scheme for multiprocessor ...
He establishes a new sufficient condition for infinite, locally finite, planar, 3-connected graphs: a finite face and odd valence. ...
Weave Realizability for D-type
[article]
2022
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Hence, the Legendrian links of D_n-type have at least as many Hamiltonian isotopy classes of Lagrangian fillings as cluster seeds in the D_n-type cluster algebra, and their geometric exchange graph for ...
Lagrangian disk surgeries contains the cluster exchange graph of D_n-type. ...
Thanks also to Youngjin Bae and Eric Zaslow for helpful conversations, and to the anonymous referee for insightful comments. ...
arXiv:2101.10306v2
fatcat:fh5ngjh7hjch5hujkdkggdtgwi
The Iso-Competition Point for Counterion Competition Binding to DNA: Calculated Multivalent Versus Monovalent Cation Binding Equivalence
1999
Biophysical Journal
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
The ionic strength effect on ICP can be expressed by a semiquantitative equation as ICP Za /ICP Zb ϭ (I a /I b ) Z , where I a , I b refers to the instance of ionic strengths and Z indicates the valence ...
At fixed ionic strength, the total DNA charge neutralization fractions ICP are equal, no matter whether the higher valence cation is divalent, trivalent, or tetravalent. ...
Manning for his insightful reading of our manuscript and Haiyan Huang for her biophysical experimental support. The authors acknowledge support from the Center for Intelligent Biomaterials. ...
doi:10.1016/s0006-3495(99)76876-1
pmid:10388744
pmcid:PMC1300316
fatcat:ww23coa26vecfm6ixeyren5sbu
Worldsheet formulations of gauge theories and gravity
[article]
1994
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
The evolution operator for states of gauge theories in the graph representation (closely related to the loop representation of Gambini and Trias, and Rovelli and Smolin) is formulated as a weighted sum ...
As examples, lattice SU(2) BF and Yang-Mills theories are expressed as worldsheet theories, and (formal) worldsheet forms of several continuum U(1) theories are given. ...
The graph states are normalized by multiplying by a factor √ 2j + 1 for each edge, including the fictitious ones in the expansion of vertices into trivalent trees. ...
arXiv:gr-qc/9412035v1
fatcat:4a3rrdzqufhztkojc4vw62nkpq
Morita classes in the homology of automorphism groups of free groups
2004
Geometry and Topology
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Topol. 3 (2003) 1167--1224], we reinterpret and generalize Morita's cycles, obtaining an unstable cycle for every connected odd-valent graph. ...
In this setting, a further generalization becomes apparent, giving cycles for objects more general than odd-valent graphs. Some of these cycles lie in the stable range. ...
For each possible pairing π , glue the paired leaves together to form a trivalent graph G π , and use the interiors of the X i to form a forest F π in G π . ...
doi:10.2140/gt.2004.8.1471
fatcat:6xstzgajtzgijidkfilmwmlh6i
The classical evaluation of relativistic spin networks
[article]
1999
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
For the graph determined by a 4-simplex this gives the evaluation as an integral over a space of geometries for a 4-simplex. ...
The evaluation of a relativistic spin network for the classical case of the Lie group SU(2) is given by an integral formula over copies of SU(2). ...
Since the contraction formula is the same for both invariants, they coincide for graphs with vertices of any valence. ...
arXiv:math/9803063v3
fatcat:jwzyjqnx7rbwzerc2lwykzxpce
Low complexity algorithms in knot theory
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We also show, that the equivalence problem for such knots with n crossings has time complexity n (n) and is in Logspace(n) and TC^0 complexity classes. ...
We show that the genus problem for alternating knots with n crossings has linear time complexity and is in Logspace(n). ...
For the proof, and later, we will need the following additional structure on a trivalent graph with Bieulerian path. Definition 5.4. ...
arXiv:1803.04908v2
fatcat:tli55rg6i5aydoubuw5up4uupi
« Previous
Showing results 1 — 15 out of 1,543 results