A census of vertices by generations in regular tessellations of the plane.
Paul, Alice, Pippenger, Nicholas (2011)
The Electronic Journal of Combinatorics [electronic only]
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Displaying similar documents to “Planar maps as labeled mobiles.”
A census of vertices by generations in regular tessellations of the plane.
On the Vertex Separation of Maximal Outerplanar Graphs
Markov, Minko (2008)
Serdica Journal of Computing
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We investigate the NP-complete problem Vertex Separation (VS) on Maximal Outerplanar Graphs (mops). We formulate and prove a “main theorem for mops”, a necessary and sufficient condition for the vertex separation of a mop being k. The main theorem reduces the vertex separation of mops to a special kind of stretchability, one that we call affixability, of submops.
On the cutting edge: simplified planarity by edge addition.
Boyer, John M., Myrvold, Wendy J. (2004)
Journal of Graph Algorithms and Applications
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The isogonal sponges on the cubic lattice.
Gillispie, Steven B., Grünbaum, Branko (2009)
The Electronic Journal of Combinatorics [electronic only]
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Relaxed graceful labellings of trees.
Van Bussel, Frank (2002)
The Electronic Journal of Combinatorics [electronic only]
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On vertices and edges in maximum path-factors of a tree
Zdzisław Skupień, Władysław Zygmunt (1980)
Fundamenta Mathematicae
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Blueprint for a classic proof of the 4 colour theorem
Patrick Labarque (2010)
Visual Mathematics
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5-Stars of Low Weight in Normal Plane Maps with Minimum Degree 5
Oleg V. Borodin, Anna O. Ivanova, Tommy R. Jensen (2014)
Discussiones Mathematicae Graph Theory
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It is known that there are normal plane maps M5 with minimum degree 5 such that the minimum degree-sum w(S5) of 5-stars at 5-vertices is arbitrarily large. In 1940, Lebesgue showed that if an M5 has no 4-stars of cyclic type (5, 6, 6, 5) centered at 5-vertices, then w(S5) ≤ 68. We improve this bound of 68 to 55 and give a construction of a (5, 6, 6, 5)-free M5 with w(S5) = 48
On the number of planar orientations with prescribed degrees.
Felsner, Stefan, Zickfeld, Florian (2008)
The Electronic Journal of Combinatorics [electronic only]
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Regulated buildups of 3-configurations
Václav J. Havel (1994)
Archivum Mathematicum
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We deal with two types of buildups of 3-configurations: a generating buildup over a given edge set and a regulated one (according to maximal relative degrees of vertices over a penetrable set of vertices). Then we take account to minimal generating edge sets, i.e., to edge bases. We also deduce the fundamental relation between the numbers of all vertices, of all edges from edge basis and of all terminal elements. The topic is parallel to a certain part of Belousov' “Configurations...