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A recursive characterization of the 4-connected graphs

1990
*
Discrete Mathematics
*

We present

doi:10.1016/0012-365x(90)90277-o
fatcat:zw4nter46bgjhezvn7ufhajyye
*a*complete description*of**the*set*of**4*-*connected*contraction-critical*graphs*. 0012-365X/90/$03.50 0 1990-Elsevier Science Publishers B.V. (North-Holland) ... Since G -{u, v,} is*Recursive**characterization*on*the**4*-*connected**graphs*107 2-*connected*we can assume that Hz contains u2, u3. Let HI be*the*component*of*G -B containing ul. ...*The*set r, consists*of**the**graphs*C", (*the*squares*of**the*cycles) for n 3 5 and*the*line*graphs**of**the*cubic cyclically*4*-edge-*connected**graphs*. M. ...##
###
Recursive Euler and Hamilton Paths

1976
*
Proceedings of the American Mathematical Society
*

There are even particularly simple classes

doi:10.2307/2041731
fatcat:nmdiuv3c75bpxjdmnich3cqhge
*of**connected*, planar, highly*recursive**graphs*for which we can show there is no effective way to decide about*the*existence*of*Euler or Hamilton paths. ... However, we obtain*the*following contrast: If*a*highly*recursive**graph*has an Euler path we can effectively find*a**recursive*Euler path; whereas, there is*a*planar, highly*recursive**graph*with Hamilton ... Manaster regarding*the*topics*of*this paper and wishes to thank*the*referee for numerous suggestions and corrections. ...##
###
Recursive Euler and Hamilton paths

1976
*
Proceedings of the American Mathematical Society
*

There are even particularly simple classes

doi:10.1090/s0002-9939-1976-0416888-0
fatcat:7pbxqymnhfedlmmohyxlefgmbm
*of**connected*, planar, highly*recursive**graphs*for which we can show there is no effective way to decide about*the*existence*of*Euler or Hamilton paths. ... However, we obtain*the*following contrast: If*a*highly*recursive**graph*has an Euler path we can effectively find*a**recursive*Euler path; whereas, there is*a*planar, highly*recursive**graph*with Hamilton ... Manaster regarding*the*topics*of*this paper and wishes to thank*the*referee for numerous suggestions and corrections. ...##
###
Page 3146 of Mathematical Reviews Vol. , Issue 2000e
[page]

2000
*
Mathematical Reviews
*

In this article Kierstead surveys

*the*topics*of**recursive**graph*col- oring, on-line*graph*coloring, and*the*strong*connection*between them.*The*article provides*a*thorough introduction. ...*A**graph*G = (V, E) is highly*recursive*if G is*recursive*,*the*degree*of*each vertex x, d(x), is finite, and 6 is*a**recursive*function. ...##
###
Chromatic polynomials of generalized trees

1988
*
Discrete Mathematics
*

*The*smallest q-tree (q 5 1) is

*the*complete

*graph*K, on q vertices. ... This paper is

*a*survey

*of*results on chromatic polynomials

*of*

*graphs*which are generalizations

*of*trees. In particular, chromatic polynomials

*of*q-trees will be discussed. ... Their proof

*of*this theorem is based on Kuratowski's

*characterization*

*of*non-planar

*graphs*in terms

*of*KS and K3,3 homeomorphs, Chao and Zhao's

*characterization*(see [

*4*] )

*of*two-

*connected*

*graphs*containing ...

##
###
A linear algorithm to recognize maximal generalized outerplanar graphs

1997
*
Mathematica Bohemica
*

D After we have

doi:10.21136/mb.1997.126148
fatcat:vd3go4numfgszdtpr3o32cinxu
*characterized*3-*connected*mgo*graphs*, it is straightforward to check*the**characterization*in*the*2-*connected*case. Lemma 2. ... During*the*backtrack*of**the*algorithm, condition*4*is tested and*the**recursion*ends when*the*situation*of*Lemma 1 or Lemma 2 occurs. ...##
###
Characterizing 2-Trees Relative to Chordal and Series-Parallel Graphs

2021
*
Theory and Applications of Graphs
*

*The*2-

*connected*2-tree

*graphs*are defined as being constructible from

*a*single 3cycle by

*recursively*appending new degree-2 vertices so as to form 3-cycles that have unique edges in common with

*the*existing ... These are also precisely

*the*2-

*connected*

*graphs*that are simultaneously chordal and series-parallel, where these latter two better-known types

*of*

*graphs*have themselves been both

*characterized*and applied ... These 2 * -trees are defined

*recursively*, now starting from any 2-

*connected*complete bipartite

*graph*instead

*of*from

*a*triangle, and they are

*characterized*in [8] by being

*the*bipartite

*graphs*that are ...

##
###
Enumeration of P 4 -Free Chordal Graphs

2003
*
Graphs and Combinatorics
*

*The*corresponding unlabelled

*graphs*are in 1-1 correspondence with unlabelled rooted trees on

*the*same number

*of*vertices. ... These

*graphs*correspond to rooted trees in which no vertex has exactly one child, and each vertex has been expanded to

*a*clique. Some properties

*of*random

*graphs*

*of*this type are also derived. ...

*The*

*characterization*

*of*P

*4*-free chordal

*graphs*given in [10] suffices to show that these unlabelled

*connected*

*graphs*correspond to unlabelled rooted trees. ...

##
###
On cyclically orientable graphs

2008
*
Discrete Mathematics
*

*The*authors obtained several nice

*characterizations*

*of*CO-

*graphs*, being motivated primarily by their applications in cluster algebras. ... We show that

*the*edge maximal CO-

*graphs*are 2-trees; that is, G = (V , E) is

*a*2-tree if and only if G is CO and G = (V , E ) is not CO whenever E is

*a*proper subset

*of*E . ... Acknowledgments I am thankful to Andrei Zelevinsky who brought to my attention

*the*CO-

*graphs*and some unpublished results in this area, to David Speyer for

*the*reference to his preprint, to Endre Boros ...

##
###
A Lex-BFS-based recognition algorithm for Robinsonian matrices

2017
*
Discrete Applied Mathematics
*

We present

doi:10.1016/j.dam.2017.01.027
fatcat:zghgtteo5bd3hib2vhja6i4u6q
*a*new polynomial time algorithm to recognize Robinsonian matrices based on*a*new*characterization**of*Robinsonian matrices in terms*of*straight enumerations*of*unit interval*graphs*. ... When applied to*a*nonnegative symmetric n × n matrix with m nonzero entries and given as*a*weighted adjacency list, it runs in O(d(n + m)) time, where d is*the*depth*of**the**recursion*tree, which is at ... Acknowledgements This work was supported by*the*Marie Curie Initial Training Network "Mixed Integer Nonlinear Optimization" (MINO) grant no. 316647. ...##
###
A Lex-BFS-Based Recognition Algorithm for Robinsonian Matrices
[chapter]

2015
*
Lecture Notes in Computer Science
*

We present

doi:10.1007/978-3-319-18173-8_24
fatcat:mjsimamdevf3lft5fvvfpbe2mi
*a*new polynomial time algorithm to recognize Robinsonian matrices based on*a*new*characterization**of*Robinsonian matrices in terms*of*straight enumerations*of*unit interval*graphs*. ... When applied to*a*nonnegative symmetric n × n matrix with m nonzero entries and given as*a*weighted adjacency list, it runs in O(d(n + m)) time, where d is*the*depth*of**the**recursion*tree, which is at ... Acknowledgements This work was supported by*the*Marie Curie Initial Training Network "Mixed Integer Nonlinear Optimization" (MINO) grant no. 316647. ...##
###
Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations

2018
*
Entropy
*

We review, study and apply

doi:10.3390/e20070534
pmid:33265623
fatcat:pmg65kxoabaqbadiarbiwzpr3m
*a*method for approximating*the*algorithmic complexity (also known as Kolmogorov–Chaitin complexity)*of**graphs*and networks based on*the*concept*of*Algorithmic Probability (AP ... AP is*a*concept (and method) capable*of**recursively*enumerate all properties*of*computable (causal) nature beyond statistical regularities. ... Every convex polyhedron can be represented in*the*plane or on*the*surface*of**a*sphere by*a*three-*connected*planar*graph*. ...##
###
Clique cycle transversals in graphs with few P₄'s

2013
*
Discrete Mathematics & Theoretical Computer Science
*

This work considers

doi:10.46298/dmtcs.616
fatcat:o4tvg27uvjcnpaxizvwqsuqje4
*the*problem*of**characterizing*extended P4-laden*graphs*admitting*a*cct. ... We*characterize*such*graphs*by means*of**a*finite family*of*forbidden induced subgraphs, and present*a*linear-time algorithm to recognize them. ...*The*p-*connected*components, or simply p-components,*of**a**graph*are*the*maximal induced subgraphs which are p-*connected*. ...##
###
Minimum energy path planning for ad hoc networks

2006
*
IEEE Wireless Communications and Networking Conference, 2006. WCNC 2006.
*

We

doi:10.1109/wcnc.2006.1683479
dblp:conf/wcnc/ChenL06
fatcat:qo47fhw74fffhfxeb57t67lrpm
*characterize*this problem and introduce two algorithms.*The*first is*a**recursive*algorithm useful for problems with one communication node. ... We demonstrate*the*applicability*of**the*minimum energy path planning problem and how*the*discretized*graph*algorithm can be used in*a*more general context through an example. ...*A**4*-*connected**graph*does not naturally allow*the*direct sn*d path*of*energy 1.8856 shown in Figure 3-3b because such*a*path moves at T = 7r/*4*and T = 77r/*4*and*a**4*-*connected**graph*constrains*the*path to ...##
###
A time bound on the materialization of some recursively defined views

1986
*
Algorithmica
*

*A*virtual relation (or view) can be defined with

*a*

*recursive*Horn clause that is

*a*function

*of*one or more base relations. ... Considering

*a*restricted class

*of*

*recursive*Horn clauses, we give necessary and sufficient conditions for members

*of*

*the*class to have this bound. ... Hence, for any path in

*the*

*a*-

*graph*there exists another one in

*the*

*a*'-

*graph*with

*the*same weight and vice-versa. [] Also, every (

*connected*) component

*of*

*the*

*graph*

*of*some simple

*recursive*Horn clause

*a*...

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