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

##
###
On two equimatchable graph classes

2003
*
Discrete Mathematics
*

In this paper, we use the Gallai-Edmonds decomposition theory for matchings to determine the

doi:10.1016/s0012-365x(02)00813-0
fatcat:flkrk7vp2zgt3ea2fyzf4hwh4a
*equimatchable*members of*two*important*graph**classes*. ... We ÿnd that there are precisely 23 3-connected planar*graphs*(i.e., 3-polytopes) which are*equimatchable*and that there are only*two*cubic*equimatchable**graphs*. ... Acknowledgements The authors wish to thank*one*of the referees for spotting a aw in our original proof of Lemma 1.10. ...##
###
Edge-Stable Equimatchable Graphs
[article]

2018
*
arXiv
*
pre-print

We are interested in

arXiv:1602.09127v3
fatcat:ustumxxivzbojdckroqjfgygli
*equimatchable**graphs*such that the removal of any edge from the*graph*preserves the*equimatchability*. ... We call an*equimatchable**graph*G edge-stable if G∖e, that is the*graph*obtained by the removal of edge e from G, is also*equimatchable*for any e ∈ E(G). ... We note that*equimatchable**graphs*are closely related to a well-studied*graph**class*called well-covered*graphs*. ...##
###
Critical Equimatchable Graphs
[article]

2022
*
arXiv
*
pre-print

We show that apart from

arXiv:2202.07929v1
fatcat:vypbbeuc3fdl7hgsk7pwuhrvba
*two*simple cases, namely bipartite ECE-*graphs*and even cliques, all ECE-*graphs*are 2-connected factor-critical. ... Our result provides a partial answer to an open question posed by Levit and Mandrescu*on*the characterization of well-covered*graphs*with no shedding vertex. ... For each*class*,*one*can check that the removal of no independent set of size 3 leaves a*graph*with a perfect matching, proving*equimatchability*by Lemma 2.6. ...##
###
Triangle-Free Equimatchable Graphs
[article]

2021
*
arXiv
*
pre-print

A

arXiv:1807.09520v2
fatcat:kd4ewissybe3fhgkgy7btxa23a
*graph*is called*equimatchable*if all of its maximal matchings have the same size. Frendrup et al. [8] provided a characterization of*equimatchable**graphs*with girth at least 5. ... In this paper, we extend this result by providing a complete structural characterization of*equimatchable**graphs*with girth at least 4, i.e.,*equimatchable**graphs*with no triangle, by identifying the*equimatchable*... We then discuss the*class*of factor-critical*equimatchable*triangle-free*graphs*. In Section 4, we structurally characterize this*graph**class*by identifying*graph*families in this*class*. ...##
###
Linear Time Recognition of Equimatchable Split Graphs
[article]

2019
*
arXiv
*
pre-print

*On*the other hand, G is called as a split

*graph*if its vertices can be partitioned into

*two*subsets for which

*one*of them forms a clique whereas the second forms an independent set. ... We will give a linear time algorithm for recognition of

*equimatchable*split

*graphs*. ... Prof. at Bogaziçi University) for introducing me

*equimatchable*

*graphs*and giving me this problem. ...

##
###
Equimatchable factor-critical graphs and independence number 2
[article]

2015
*
arXiv
*
pre-print

It is known that any 2-connected

arXiv:1501.07549v1
fatcat:5a3m3yoh6zbsxlifaxc5d5b2km
*equimatchable**graph*is either bipartite, or factor-critical, and that these*two**classes*are disjoint. ...*On*the other hand, since every 2-connected odd*graph*with independence number 2 is*equimatchable*, we get the following result. ...*Equimatchable**graphs*G such that G ∪ {e} is*equimatchable*for every edge e of the complement G of G are further investigated in [3] , together with other extremal*classes*of*equimatchable**graphs*. ...##
###
On two extensions of equimatchable graphs
[article]

2016
*
arXiv
*
pre-print

In this work we introduce

arXiv:1612.08531v1
fatcat:t5czsuzyk5e3zgzfddi3ksnnbu
*two*extensions of the property of*equimatchability*by defining*two*new*graph*parameters that measure how far a*graph*is from being*equimatchable*. ... A*graph*is said to be*equimatchable*if all its maximal matchings are of the same size. ... In this paper we generalize the property of*equimatchability*of*graphs*in*two*further ways by introducing*two**graph*parameters measuring how far a*graph*is from being*equimatchable*. ...##
###
Equimatchable bipartite graphs

2020
*
Discussiones Mathematicae Graph Theory
*

[A note

doi:10.7151/dmgt.2356
fatcat:msuou63swzfvdkqqdbopditip4
*on**equimatchable**graphs*, Australas. J. ... For an*equimatchable**graph*, an edge is said to be a critical-edge if the*graph*obtained by the removal of this edge is not*equimatchable*. ... The*class*of*equimatchable**graphs*is separated into*two*complementary subclasses, namely factor-critical and non-factor-critical*equimatchable**graphs*. ...##
###
Totally equimatchable graphs

1997
*
Discrete Mathematics
*

A subset X of vertices and edges of a

doi:10.1016/s0012-365x(96)00062-3
fatcat:cqia5za3mvctbdg6let2hhh2ci
*graph*G is totally matching if no*two*elements of X are adjacent or incident. ... In this paper we determine all*graphs*in which every maximal total matching is maximum. ... A connected*graph*is totally*equimatchable*if and only if it is*one*of the*graphs*Claim 1. Let M be a maximum matching of G. ...##
###
Equimatchable claw-free graphs

2018
*
Discrete Mathematics
*

In this paper, we provide, to the best of our knowledge, the first characterization of claw-free

doi:10.1016/j.disc.2018.06.043
fatcat:krsy7k6bxfgwrkmq7hqmyzezre
*equimatchable**graphs*by identifying the*equimatchable*claw-free*graph*families. ... A*graph*is*equimatchable*if all of its maximal matchings have the same size. A*graph*is claw-free if it does not have a claw as an induced subgraph. ... subgraph of them; otherwise, H has to be compared to each*one*of these*graphs*and their relevant subgraphs, where each comparison takes constant time. ...##
###
2-connected equimatchable graphs on surfaces
[article]

2013
*
arXiv
*
pre-print

We use this result to improve the upper bounds

arXiv:1312.3423v1
fatcat:747xzsp5f5hp7bdhi5cddgazei
*on*the maximum size of $2$-connected*equimatchable*factor-critical*graphs*embeddable in the orientable surface of genus $g$ to $4\sqrt g+17$ if $g\le 2$ and ... A*graph*$G$ is*equimatchable*if any matching in $G$ is a subset of a maximum-size matching. It is known that any $2$-connected*equimatchable**graph*is either bipartite or factor-critical. ... Therefore, these*two**classes*are disjoint. All 3-connected planar*equimatchable**graphs*are characterised in [7] -there are 23 such*graphs*and none of them is bipartite. ...##
###
Page 6786 of Mathematical Reviews Vol. , Issue 87m
[page]

1987
*
Mathematical Reviews
*

The author further shows that if G is an

*equimatchable*factor-critical*graph*having connectivity 2 and vertex cut-set S = {s,,82}, then G—S has exactly*two*components,*one*of even order and the other of ... Isolated vertices or loops are circuits with*one*vertex, and edges or*two*vertices joined by a pair of edges are circuits with*two*vertices. ...##
###
On Minimum Maximal Distance-k Matchings

2016
*
Electronic Notes in Discrete Mathematics
*

We introduce the

doi:10.1016/j.endm.2016.11.011
fatcat:j3gvr6p2anbtdalx6sid6lqgki
*class*of k-*equimatchable**graphs*which is an edge analogue of k-equipackable*graphs*. We prove that the recognition of k-*equimatchable**graphs*is co-NP-complete for any fixed k ≥ 2. ... We provide a simple characterization for the*class*of strongly chordal*graphs*with equal k-packing and k-domination numbers. ... We also thank anonymous reviewers for their numerous helpful comments*on*the preliminary versions of this paper. ...##
###
On Minimum Maximal Distance-k Matchings
[article]

2017
*
arXiv
*
pre-print

We introduce the

arXiv:1602.04581v4
fatcat:oxeev4lkzvcwze4hwht5clk4ya
*class*of k-*equimatchable**graphs*which is an edge analogue of k-equipackable*graphs*. We prove that the recognition of k-*equimatchable**graphs*is co-NP-complete for any fixed k > 2. ... We provide a simple characterization for the*class*of strongly chordal*graphs*with equal k-packing and k-domination numbers. ... We also thank anonymous reviewers for their numerous helpful comments*on*the preliminary versions of this paper. ...##
###
Well-indumatched Trees and Graphs of Bounded Girth
[article]

2019
*
arXiv
*
pre-print

We also show that, although the recognition of well-indumatched

arXiv:1903.03197v2
fatcat:uqxica22f5fmzminvnjjk7za5y
*graphs*is known to be co-NP-complete in general,*one*can recognize in polynomial time well-indumatched*graphs*where the size of maximal induced ...*On*the other hand, there are infinitely many well-indumatched unicyclic*graphs*of girth k, where k is in 3, 5, 7 or k is an even integer greater than 2. ... Some other*graph**classes*that could be investigated in this direction are interval*graphs*, claw-free*graphs*or*equimatchable**graphs*. ...
« Previous

*Showing results 1 — 15 out of 41 results*