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
Toughness, hamiltonicity and split graphs
1996
Discrete Mathematics
Preserved Fulltext
First, we consider properties of graph classes related to hamiltonicity, traceability and toughness concepts and display some algorithmic consequences. ...
Related to Chvfital's famous conjecture stating that every 2-tough graph is hamiltonian, we study the relation of toughness and hamiltonieity on special classes of graphs. ...
We are going to show that our three properties of graph classes are indeed strongly related to each other (without the need of any structural properties of a certain graph class).
Theorem 2.2. ...
doi:10.1016/0012-365x(95)00190-8
fatcat:3vqxxzp2sfc5tlxhqv6xefmt3m
Graph connectivity and binomial edge ideals
2016
Proceedings of the American Mathematical Society
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 relate homological properties of a binomial edge ideal J G to invariants that measure the connectivity of a simple graph G. ...
Specifically, we show if R/J G is a Cohen-Macaulay ring, then graph toughness of G is exactly 1 2 . We also give an inequality between the depth of R/J G and the vertexconnectivity of G. ...
Graph toughness and binomial edge ideals. In this subsection we establish relations between graph toughness and different aspects related to the dimension and depth of a binomial edge ideal. ...
doi:10.1090/proc/13241
fatcat:jbyiuwq7mjakrahf5tylhrcwq4
On the shortness exponent of 1-tough, maximal planar graphs
1996
Discrete 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 2019; you can also visit the original URL.
The file type is application/pdf.
It is shown that the shortness exponent of the class of l-tough, maximal planar graphs is at most log, 5. ...
The non-Hamiltonian, l-tough, maximal planar graph with a minimum number of vertices is presented. 0012-365X/96/$15.00 0 1996-Elsevier Science B.V. All rights reserved SSDI 0012-365X(94)00356-4 ...
Acknowledgements The author would like to thank the referees for making a number of suggestions which resulted in a much improved paper and for pointing out an oversight in one of its earlier versions. ...
doi:10.1016/0012-365x(94)00356-n
fatcat:j6heulytrrbbxmu26qbbldm4wa
Minimally toughness in special graph classes
[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.
A graph is minimally t-tough, if the toughness of the graph is t and the deletion of any edge from the graph decreases the toughness. ...
A graph is called t-tough, if the removal of any cutset S leaves at most |S|/t components. The toughness of a graph is the largest t for which the graph is t-tough. ...
The research of the second author was supported by National Research, Development and Innovation Office NKFIH, K-124171. ...
arXiv:1802.00055v1
fatcat:lyo3gefwvfef5eidytlf2f2r74
Hamiltonian prisms on 5-chordal graphs
[article]
2016
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.
In this paper, we provide a method to find a Hamiltonian cycle in the prism of a 5-chordal graph, which is (1+ϵ)-tough, with some special conditions. ...
Corollary 2 . 2 Let G be a (1 + ǫ)-tough 5-chordal graph such that, for every 3 mutual remote edges e 1 , e 2 , e 3 of G, ...
Preliminaries The toughness of graphs is a concept introduced by Chvátal [6] , when he was doing research on Hamiltonicity of graphs. ...
arXiv:1603.01371v1
fatcat:2v77fngjd5eyte753qwwczdnca
Local Topological Toughness and Local Factors
2007
Graphs and 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 2017; you can also visit the original URL.
The file type is application/pdf.
We prove, that besides this the topological toughness has nearly all known nice properties of Katona's edge-toughness and therefore is worth to be considered. ...
We localize and strengthen Katona's idea of an edge-toughness to a local topological toughness. We disprove a conjecture of Katona concerning the connection between edgetoughness and factors. ...
Let N C be the set of graphs not being 1-tough, N E be the set of graphs not being 1-edge-tough and N T be the set of graphs not being topological 1-tough. ...
doi:10.1007/s00373-007-0736-x
fatcat:wiijwm5uazfi3novrj72b5zj5e
Page 61 of Mathematical Reviews Vol. , Issue 2001A
[page]
2001
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.
(H-AOS; Budapest)
Properties of edge-tough graphs. (English summary)
Graphs Combin. 15 (1999), no. 3, 315-325. ...
It is known that a 2f-tough graph is always t-edge-tough. The author proves that this is tight in the following sense: For any 0 < e < 1, there exists a (27 — €)-tough graph that is not t-edge-tough. ...
Properties of minimally t-tough graphs
[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 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
A graph G is minimally t-tough if the toughness of G is t and the deletion of any edge from G decreases the toughness. ...
Kriesell conjectured that for every minimally 1-tough graph the minimum degree δ(G)=2. We show that in every minimally 1-tough graph δ(G)<n+2/3. ...
All authors are partially supported by the grant of the National Research, Development and Innovation Office -NKFIH, No. 108947. ...
arXiv:1604.02746v2
fatcat:d5eolkm3mvaejf3o565o5t4cb4
Toughness and Delaunay triangulations
1990
Discrete & Computational Geometry
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.
A graph G is 1-tough if for any set P of vertices, c(G -P) < I GI, where c(G -P) is the number of components of the graph obtained by removing P and all attached edges from G, and I GI is the number of ...
This property arises in the study of Hamiltonian graphs: all Hamiltonian graphs are 1-tough, but not conversely. ...
Douglas West and Herbert Edelsbrunner pointed out to me the connection between 1-toughness and perfect matchings. ...
doi:10.1007/bf02187810
fatcat:twkcz73tezdmxnygspfhdrdc6u
Graph Connectivity and Binomial Edge Ideals
[article]
2016
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.
We relate homological properties of a binomial edge ideal J_G to invariants that measure the connectivity of a simple graph G. ...
Specifically, we show if R/J_G is a Cohen-Macaulay ring, then graph toughness of G is exactly 1/2. We also give an inequality between the depth of R/J_G and the vertex-connectivity of G. ...
The second author gratefully acknowledges the support of the National Science Foundation for support through Grant DMS-1502282. ...
arXiv:1605.00314v1
fatcat:3xmhuuaztre4hivlt5jbwuvkrm
Page 3571 of Mathematical Reviews Vol. , Issue 91G
[page]
1991
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.
Some structural properties involving removable edges are developed, including the fact that in a 3-connected graph of order at least 5, at least two edges of every 3-cycle are removable, as is at least ...
Carsten Thomassen (DK-TUD)
91g:05085 05C45 05C40
Dawes, Robin W. (3-QEN-C); Rodrigues, Marion G. (3-QEN-C) Properties of 1-tough graphs.
J. Combin. Math. Combin. Comput. 7 (1990), 153-159. ...
Properties of minimally t-tough graphs
2018
Discrete 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.
A graph G is minimally t-tough if the toughness of G is t and the deletion of any edge from G decreases the toughness. ...
Kriesell conjectured that for every minimally 1-tough graph the minimum degree δ(G) = 2. We show that in every minimally 1-tough graph δ(G) ≤ n 3 + 1. ...
All authors are partially supported by the grant of the National Research, Development and Innovation Office -NKFIH, No. 108947. ...
doi:10.1016/j.disc.2017.08.033
fatcat:qjafkqrx35hbnn2sk5z7kpc7t4
Toughness and hamiltonicity in k-trees
2007
Discrete 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 2019; you can also visit the original URL.
The file type is application/pdf.
By a result of Chen et al. 18-tough chordal graphs are hamiltonian, and by a result of Bauer et al. there exist nontraceable chordal graphs with toughness arbitrarily close to 7 4 . ...
We consider toughness conditions that guarantee the existence of a hamiltonian cycle in k-trees, a subclass of the class of chordal graphs. ...
Thus F + {xv, yv} is a 1-tough spanning 2-tree of G containing every edge of C. ...
doi:10.1016/j.disc.2005.11.051
fatcat:ngx4nw6sfvb7jk4jvgcf2jyy4u
Page 8943 of Mathematical Reviews Vol. , Issue 2003m
[page]
2003
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.
Although connectivity and edge-connectivity are good measures, many of these graphs have stronger properties. ...
Summary: “A cut edge in a graph G is an edge whose removal increases the number of connected components of G. ...
2-walks in 2-tough 2k2-free graphs
[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.
Other Versions
In this paper, we prove that in every 2-tough 2K_2-free graph, there is a 2-walk. ...
On 2K 2 -free graphs We present several structural properties of 2K 2 -free graphs which turn out to be very useful in the proof of the main theorem. ...
Every 1/(k − 2)-tough graph has a k-walk. In particular every 1-tough graph has a 3-walk. ...
arXiv:1408.3380v3
fatcat:pcrwqjzmfrcbhgron6iti3mfsy
« Previous
Showing results 1 — 15 out of 14,718 results