
On the tenacity of cycle permutation graph
A special class of cubic graphs is the cycle permutation graphs. A cycle...
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Improved Bounds for Guarding Plane Graphs with Edges
An "edge guard set" of a plane graph G is a subset Γ of edges of G such ...
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Dynamic Schnyder Woods
A realizer, commonly known as Schnyder woods, of a triangulation is a pa...
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A framework for modelling Molecular Interaction Maps
Metabolic networks, formed by a series of metabolic pathways, are made o...
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Guarding Quadrangulations and Stacked Triangulations with Edges
Let G = (V,E) be a plane graph. A face f of G is guarded by an edge vw ∈...
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An Edge ExtrusionApproach to Generate Extruded MiuraOri and Its Double Tiling Origami Patterns
This paper proposes a family of origami tessellations called extruded Mi...
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A Game of Cops and Robbers on Graphs with Periodic EdgeConnectivity
This paper considers a game in which a single cop and a single robber ta...
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Random 2cell embeddings of multistars
By using permutation representations of maps, one obtains a bijection between all maps whose underlying graph is isomorphic to a graph G and products of permutations of given cycle types. By using statistics on cycle distributions in products of permutations, one can derive information on the set of all 2cell embeddings of G. In this paper, we study multistars – loopless multigraphs in which there is a vertex incident with all the edges. The well known genus distribution of the twovertex multistar, also known as a dipole, can be used to determine the expected genus of the dipole. We then use a result of Stanley to show that, in general, the expected genus of every multistar with n nonleaf edges lies in an interval of length 2/(n+1) centered at the expected genus of an nedge dipole. As an application, we show that the face distribution of the multistar is the same as the face distribution gained when adding a new vertex to a 2cell embedded graph, and use this to obtain a general upper bound for the expected number of faces in random embeddings of graphs.
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