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.
Filters
Edge Erasures and Chordal Graphs
[article]
2018
arXiv
pre-print
Preserved Fulltext
Other Versions
We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. ...
This leads to a characterization of chordal graphs via deletions of a sequence of exposed edges from a complete graph. ...
The authors gratefully acknowledge the support of Air Force Office of Science Research under the LRIR 15RYCOR153, MURI FA9550-10-1-0567 and FA9550-11-10223 grants, respectively. ...
arXiv:1706.04537v2
fatcat:tjwgixku2fh7hoinnmrzw4l4za
Edge erasures and chordal graphs
2021
Electronic Journal of Graph Theory and 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 2022; you can also visit the original URL.
The file type is application/pdf.
We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. ...
This leads to a characterization of chordal graphs via deletions of a sequence of exposed edges from a complete graph. ...
Acknowledgement The authors gratefully acknowledge the support of Air Force Office of Science Research under the LRIR 15RYCOR153, MURI FA9550-10-1-0567 and FA9550-11-10223 grants, respectively. ...
doi:10.5614/ejgta.2021.9.2.13
fatcat:caesmmgu5zfw5kzguolhu5kxne
Extendable shellability for d-dimensional complexes on d+3 vertices
[article]
2021
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 2021; you can also visit the original URL.
The file type is application/pdf.
Other Versions
The proof involves considering the structure of 'exposed' edges in chordal graphs as well as a connection to linear quotients of quadratic monomial ideals. ...
Suppose G is a chordal graph and xy ∈ ∂G is an exposed edge. ...
In [7] it is shown that a graph G on vertex set [n] = {1, 2, . . . , n} is chordal if and only if G can be obtained from the complete graph K n via a sequence of erasures. ...
arXiv:1908.07155v2
fatcat:htpofilfufcbpaz2enhmqe673i
Extendable Shellability for $d$-Dimensional Complexes on $d+3$ Vertices
2020
Electronic Journal of Combinatorics
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.
The proof involves considering the structure of 'exposed' edges in chordal graphs as well as a connection to linear quotients of quadratic monomial ideals. ...
Dan Guralnik is grateful to Kod*Lab and all its members for his time there, and particularly to Daniel E. Koditschek for encouraging this collaboration. ...
Suppose G is a chordal graph and xy ∈ ∂G is an exposed edge. ...
doi:10.37236/9120
fatcat:bjgljaydzrgkxm5tfyhxonzube
Exposed circuits, linear quotients, and chordal clutters
[article]
2021
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 2021; you can also visit the original URL.
The file type is application/pdf.
Other Versions
In a recent preprint Culbertson, Guralnik, and Stiller give a new characterization of chordal graphs in terms of sequences of what they call 'edge-erasures'. ...
A graph G is said to be chordal if it has no induced cycles of length four or more. ...
Macaulay2 [17] was used extensively to compute examples and we have included calculations in figures below. ...
arXiv:1812.08128v3
fatcat:xanpoyb6hbec5o5elm2jt5s6vi
Convergence of loop erased random walks on a planar graph to a chordal SLE(2) curve
[article]
2014
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.
that the loop erasure of the conditioned walk converges, as δ↓ 0, to the chordal SLE_2 that connects a and b in D, provided that an invariance principle is valid for both the random walk and the dual walk ...
In this paper we consider the natural random walk on a planar graph and scale it by a small positive number δ. ...
prior to its publication and letting me include a result therein as Proposition 6.1. ...
arXiv:1408.0849v1
fatcat:hdglcbr5jjfttna5f53exfjxfy
Convergence of loop erased random walks on a planar graph to a chordal SLE(2) curve
2014
Kodai Mathematical 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.
Acknowledgments I am very thankful to my advisor, K.Uchiyama, for introducing me to this research topic, and for his encouragements and many invaluable and helpful comments. ...
I also would like to thank Tokyo Institute of Technology for providing me a wonderful environment for my life and study. Last I thank to my family for their encouragements and supports. ...
Since G δ is planar graph, S x δ can not cross the edge e, so that it cannot behave as a Brownian path and the invariance principle fails to hold. ...
doi:10.2996/kmj/1404393889
fatcat:et4p7lagt5fipn5nxbfhqfvyp4
Neighborhood Expansion Grammars
[chapter]
2000
Lecture Notes in Computer Science
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.
But, these gramamars are most e ective only to generate, and parse, strings. ...
For example, we show that restricted neighborhood expansion grammars capture the essence of nite state and context free phrase structure grammars. ...
Figure 1 : A sequence of neighborhood expansions generating chordal graphs clique), and because every chordal graph must have at least two extreme points 8, 6], every chordal graph can be so generated. ...
doi:10.1007/978-3-540-46464-8_3
fatcat:yq2ukgppgvhnxcogepa65ypznm
Multiple SLE type scaling limits: from local to global
[article]
2019
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.
We consider collections of N chordal random curves obtained from a critical lattice model on a planar graph, in the limit when a fine-mesh graph approximates a simply-connected domain. ...
These results essentially only take as input certain crossing conditions, very similar to those introduced by Kemppainen and Smirnov, and they allow the identification of scaling limits via the martingale ...
,e 2N ) that we are interested in are these conditional USTs, and the random chordal curves γ G;1 , . . . , γ G;N are the chordal graph paths consisting of the odd edges e 1 , e 3 , . . . , e 2N −1 and ...
arXiv:1903.10354v1
fatcat:irho7y4fkjgilojcwwdnmi5pg4
Conformal invariance of planar loop-erased random walks and uniform spanning trees
2004
Annals of Probability
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.
In particular, the limit exists and is conformally invariant. It follows that the scaling limit of the uniform spanning tree in a Jordan domain exists and is conformally invariant. ...
The results and proofs are not restricted to a particular choice of lattice. ...
Give n a spanning tree T of C , let T t de note the graph whose vertices are the ve rtices of c t and whose edges are those edges e t suc h th at e ¢. T. ...
doi:10.1214/aop/1079021469
fatcat:lmhxn7hjxbfpnesgewaudm3fu4
Conformal Invariance Of Planar Loop-Erased Random Walks and Uniform Spanning Trees
[chapter]
2011
Selected Works of Oded Schramm
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.
In particular, the limit exists and is conformally invariant. It follows that the scaling limit of the uniform spanning tree in a Jordan domain exists and is conformally invariant. ...
The results and proofs are not restricted to a particular choice of lattice. ...
Give n a spanning tree T of C , let T t de note the graph whose vertices are the ve rtices of c t and whose edges are those edges e t suc h th at e ¢. T. ...
doi:10.1007/978-1-4419-9675-6_30
fatcat:qvkzty2ehzd65hqndtcsy7optu
Boundary behaviour of RW's on planar graphs and convergence of LERW to chordal SLE_2
[article]
2017
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 2019; you can also visit the original URL.
The file type is application/pdf.
This paper concerns a random walk on a planar graph and presents certain estimates concerning the harmonic measures for the walk in a grid domain which estimates are useful for showing the convergence ...
We assume that the walk started at a fixed vertex of the graph satisfies the invariance principle as in Yadin and Yehudayoff [16] in which the convergence of LERW to a radial SLE is established in this ...
In this paper we are concerned with the chordal case of LERW on a planar graph as in [12] . ...
arXiv:1705.03224v1
fatcat:yhxdvobfivgwbjev2wlptbmk3u
Conformally invariant scaling limits (an overview and a collection of problems)
[article]
2006
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
Before we present the open problems, the definition of SLE will be motivated and explained, and a brief sketch of recent results will be presented. ...
There is a random graph dual to the tree, which consists of the dual edges perpendicular to primal edges not in the tree. ...
The Fortuin-Kasteleyn [28] (FK) model (a.k.a. the random cluster model) is a probability measure on the collection of all subsets of the set of edges E of a finite graph G = (V, E). ...
arXiv:math/0602151v2
fatcat:glk7pdoqxbg7jcnrupbvlc5fjm
Random planar curves and Schramm-Loewner evolutions
[article]
2003
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.
We review some of the results that have been derived in the last years on conformal invariance, scaling limits and properties of some two-dimensional random curves. ...
probabilities, critical exponents) using SLE, relate SLE to planar Brownian motions (i.e. the determination of the critical exponents), planar self-avoiding walks, critical percolation, loop-erased random walks and ...
Uniform spanning trees, Wilson's algorithm Suppose that a connected finite graph G = (V, E) is given (V is the set of vertices and E is the set of edges). ...
arXiv:math/0303354v1
fatcat:uhkfpzchuvh3zjbjzhsejnatda
Topics in loop measures and the loop-erased walk
[article]
2017
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 2019; you can also visit the original URL.
The file type is application/pdf.
These are notes based on a course that I gave at the University of Chicago in Fall 2016 on "Loop measures and the loop-erased random walk." ...
Adding a self-edge Suppose that (27) holds for a graph G = (A, E) with A = {x 1 , . . . , x n } and consider a new graphG = (A,Ẽ) by adding one self-edgeẽ at x 1 . ...
Take the loop-erasure LE(S j [0, T j ]) and add those edges and vertices to the tree to formT j . ...
arXiv:1709.07531v1
fatcat:lnrax767ibgnfk67myyqtex744
« Previous
Showing results 1 — 15 out of 63 results