The planar graphs and face routing
Transfer-Efficient Face Routing Using the Planar Graphs of Neighbors in High Density WSNs
... local planar graphs of the message transfer node’s neighbors needs more location information compared with legacy face routing using local information but uses less position information than ...
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Single-face non-crossing shortest paths in planar graphs
... a planar emebdding leads to a straightforward algorithm for finding a ...connected planar-embedded graph G and the weak dual graph T of its corresponding connection graph instead of the connection graph ...
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Constant Congestion Routing of Symmetric Demands in Planar Directed Graphs
... in planar graphs the best approximation up to very recently was O( √ n), with a slight improvement just announced ...undirected graphs via the notion of ...
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Convex drawings of hierarchical planar graphs and clustered planar graphs
... hierarchical graphs and clustered graphs. Hierarchical graphs and clustered graphs are useful graph models with structured relational ...Hierarchical graphs are graphs with ...
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Quartic planar graphs
... of graphs to either be a small finite collection graphs, or else some infinite family for which there is a general, explicit description such as the cycles, prisms, or pseudo-double ...of graphs from ...
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Connectivity of Planar Graphs
... The algorithm we present here has been optimized using Schnyder’s decom- positions, the definition of which we shall recall here: Definition 4.1 (Schnyder, [14]) Let G be a maximal planar graph and {r 1 , r 2 , r ...
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Planar Graphs, Regular Graphs, Bipartite Graphs and Hamiltonicity
... The advantage of cubic graphs (every vertex of degree 3) when looking for a Hamiltonian cycle is that if two edges incident with a vertex are in a Hamiltonian cycle, then the [r] ...
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PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS
... Chapter 1 Introduction Within the branch of combinatorics exists a field of mathematics called graph theory. Graphs can be used to model many everyday circumstances, such as transporta- tion networks and ...
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On Planar Greedy Drawings of 3-Connected Planar Graphs
... greedy routing scheme have been proposed; see, ...greedy routing protocol has two disadvantages which limit its ...geographic routing in order to overcome the above ...greedy routing protocol ...
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Planar Graphs with Topological Constraints
... Graphs whose vertices and edges represent spatial entities such as road maps or subway maps often induce some natural meaning to the faces and regions of their embeddings as well. In this case, topological ...
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Optimal 1-planar graphs
... It is known that for any orientable surface S g other than the sphere, there exists an optimal 1-planar graph which can be embedded on S g as a triangulation. In this paper, we prove that for any orientable ...
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On the diameter of random planar graphs
... for planar graphs contrast with the so-called “subcritical” graph families, such as trees, outerplanar graphs, and series-parallel graphs, where the diameter is in the interval (n 1/2−ǫ , n ...
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On the diameter of random planar graphs
... for planar maps mentioned ...3-connected planar graphs, because they have a unique embedding in the ...connected planar graphs, but this is not ...
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Geometric Number of Planar Graphs
... a planar graph if it is possible to represent it in the plane such that no two edges of the graph intersect except possibly at a vertex to which they are both ...of planar graph G in a plane is a ...
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Recognizing Planar Laman Graphs
... Our algorithms do not provide any certificate for their correctness. This could be a Henneberg sequence [17] or a decomposition into two acyclic subgraphs [7]. We do not know how to compute either of these faster than ...
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Wheel Planar Graphs in Topology
... Consider the n+1 case, we can choose an edge e={u, v} such that G/e with the identified vertex v is still 3-connected. This means that G-v is 2-connected. Now consider the cycle C containing all the neighbours of v. ...
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On acyclic colorings of planar graphs
... and Berman [1] proved the result for 7 colors. As it was pointed out by Grünbaum, the positive solution of his problem absorbs some results from [3,4,6,9,11], in which coverings of planar graphs by forests ...
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Triangle-Free Planar Graphs as Segment Intersection Graphs
... Enlarging a segment means to increase its length, and obviously we also need to increase the length of other segments of the representation and make a translation of other segments without modifying their length. With ...
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Projective-Planar Signed Graphs and Tangled Signed Graphs
... Proof of Claim: Let v be a vertex of attachment of B off of τ . To prove our claim we need only show that there is no path from v to m or g that does not pass through {b, h, c}. First suppose v is on τ 1 and suppose by ...
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An Maxflow Algorithm for Directed Planar Graphs
... 7.2 Convergence of TestGraph 7 RESULTS node. The graphs are created such that there are s-t-paths which are close the the possible maximum of n − 1 arcs. Since every node is reachable from the source node and it ...
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