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A recursive characterization of the 4-connected graphs

Nicola Martinov
1990 Discrete Mathematics  
We present 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.  ... 
doi:10.1016/0012-365x(90)90277-o fatcat:zw4nter46bgjhezvn7ufhajyye

Recursive Euler and Hamilton Paths

Dwight R. Bean
1976 Proceedings of the American Mathematical Society  
There are even particularly simple classes 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.  ... 
doi:10.2307/2041731 fatcat:nmdiuv3c75bpxjdmnich3cqhge

Recursive Euler and Hamilton paths

Dwight R. Bean
1976 Proceedings of the American Mathematical Society  
There are even particularly simple classes 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.  ... 
doi:10.1090/s0002-9939-1976-0416888-0 fatcat:7pbxqymnhfedlmmohyxlefgmbm

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

Earl Glen Whitehead
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  ... 
doi:10.1016/0012-365x(88)90231-2 fatcat:v5opf5ppevetjekqjjs2nkeayi

A linear algorithm to recognize maximal generalized outerplanar graphs

José Cáceres, Alberto Márquez
1997 Mathematica Bohemica  
D After we have 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.  ... 
doi:10.21136/mb.1997.126148 fatcat:vd3go4numfgszdtpr3o32cinxu

Characterizing 2-Trees Relative to Chordal and Series-Parallel Graphs

Terry McKee, Wright State University
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  ... 
doi:10.20429/tag.2021.080104 fatcat:vhhhpqozhbfefgguwas25cd43i

Enumeration of P 4 -Free Chordal Graphs

Robert Castelo, Nick Wormald
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.  ... 
doi:10.1007/s00373-002-0513-9 fatcat:czh5ifswcfb7vb7qapoqhwcw7u

On cyclically orientable graphs

Vladimir Gurvich
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  ... 
doi:10.1016/j.disc.2007.03.055 fatcat:uodgqi3aifd7tdgu6kiykdpmqq

A Lex-BFS-based recognition algorithm for Robinsonian matrices

M. Laurent, M. Seminaroti
2017 Discrete Applied Mathematics  
We present 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.  ... 
doi:10.1016/j.dam.2017.01.027 fatcat:zghgtteo5bd3hib2vhja6i4u6q

A Lex-BFS-Based Recognition Algorithm for Robinsonian Matrices [chapter]

Monique Laurent, Matteo Seminaroti
2015 Lecture Notes in Computer Science  
We present 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.  ... 
doi:10.1007/978-3-319-18173-8_24 fatcat:mjsimamdevf3lft5fvvfpbe2mi

Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations

Hector Zenil, Narsis Kiani, Jesper Tegnér
2018 Entropy  
We review, study and apply 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.  ... 
doi:10.3390/e20070534 pmid:33265623 fatcat:pmg65kxoabaqbadiarbiwzpr3m

Clique cycle transversals in graphs with few P₄'s

Raquel Bravo, Sulamita Klein, Loana Tito Nogueira, Fábio Protti
2013 Discrete Mathematics & Theoretical Computer Science  
This work considers 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.  ... 
doi:10.46298/dmtcs.616 fatcat:o4tvg27uvjcnpaxizvwqsuqje4

Minimum energy path planning for ad hoc networks

Danjie Chen, P.J. Lin
2006 IEEE Wireless Communications and Networking Conference, 2006. WCNC 2006.  
We 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  ... 
doi:10.1109/wcnc.2006.1683479 dblp:conf/wcnc/ChenL06 fatcat:qo47fhw74fffhfxeb57t67lrpm

A time bound on the materialization of some recursively defined views

Yannis E. Ioannidis
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  ... 
doi:10.1007/bf01840452 fatcat:poxhsv5j5fdcfbgvs46ggfhat4
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