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Recent Excluded Minor Theorems for Graphs
 IN SURVEYS IN COMBINATORICS, 1999 267 201222. THE ELECTRONIC JOURNAL OF COMBINATORICS 8 (2001), #R34 8
, 1999
"... A graph is a minor of another if the first can be obtained from a subgraph of the second by contracting edges. An excluded minor theorem describes the structure of graphs with no minor isomorphic to a prescribed set of graphs. Splitter theorems are tools for proving excluded minor theorems. We disc ..."
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Cited by 9 (0 self)
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A graph is a minor of another if the first can be obtained from a subgraph of the second by contracting edges. An excluded minor theorem describes the structure of graphs with no minor isomorphic to a prescribed set of graphs. Splitter theorems are tools for proving excluded minor theorems. We discuss splitter theorems for internally 4connected graphs and for cyclically 5connected cubic graphs, the graph minor theorem of Robertson and Seymour, linkless embeddings of graphs in 3space, Hadwiger’s conjecture on tcolorability of graphs with no Kt+1 minor, Tutte’s edge 3coloring conjecture on edge 3colorability of 2connected cubic graphs with no Petersen minor, and Pfaffian orientations of bipartite graphs. The latter are related to the even directed circuit problem, a problem of Pólya about permanents, the 2colorability of hypergraphs, and signnonsingular matrices.
Nonhamiltonian 3connected cubic planar graphs
 SIAM J. Disc. Math
"... We establish that every cyclically 4connected cubic planar graph of order at most 40 is hamiltonian. Furthermore, this bound is determined to be sharp and we present all nonhamiltonian such graphs of order 42. In addition we list all nonhamiltonian cyclically 5connected cubic planar graphs of orde ..."
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Cited by 6 (3 self)
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We establish that every cyclically 4connected cubic planar graph of order at most 40 is hamiltonian. Furthermore, this bound is determined to be sharp and we present all nonhamiltonian such graphs of order 42. In addition we list all nonhamiltonian cyclically 5connected cubic planar graphs of order at most 52 and all nonhamiltonian 3connected cubic planar graphs of girth 5 on at most 46 vertices. That all 3connected cubic planar graphs on at most 176 vertices and with face size at most 6 are hamiltonian is also verified. 1 Introduction. In this paper we describe an investigation (making much use of computation) of cyclically kconnected cubic planar graphs (CkCPs) for k = 4, 5 and report the results. We shall also have occasion to consider cubic 3connected planar graphs with no restriction on cyclic connectivity; these we refer to as C3CPs. The investigation
Recent Excluded Minor Theorems
 Surveys in Combinatorics, LMS Lecture Note Series
"... We discuss splitter theorems for internally 4connected graphs and for cyclically 5connected cubic graphs, the graph minor theorem, linkless embeddings, Hadwiger's conjecture, Tutte's edge 3coloring conjecture, and Pfaffian orientations of bipartite graphs. ..."
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Cited by 3 (1 self)
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We discuss splitter theorems for internally 4connected graphs and for cyclically 5connected cubic graphs, the graph minor theorem, linkless embeddings, Hadwiger's conjecture, Tutte's edge 3coloring conjecture, and Pfaffian orientations of bipartite graphs.
Construction of planar triangulations with minimum degree 5
, 1969
"... In this article we describe a method of constructing all simple triangulations of the sphere with minimum degree 5; equivalently, 3connected planar cubic graphs with girth 5. We also present the results of a computer program based on this algorithm, including counts of convex polytopes of minimum d ..."
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Cited by 3 (1 self)
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In this article we describe a method of constructing all simple triangulations of the sphere with minimum degree 5; equivalently, 3connected planar cubic graphs with girth 5. We also present the results of a computer program based on this algorithm, including counts of convex polytopes of minimum degree 5. Key words: planar triangulation, cubic graph, generation, fullerene
Journal of Graph Algorithms and Applications
, 2010
"... Recursive generation of simple planar 5regular graphs and pentangulations ..."
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Recursive generation of simple planar 5regular graphs and pentangulations