planar graphs
The Liouville and the intersection properties are equivalent for planar graphs
... all neighbors x, y of the graph. For example, it is known that if a graph admits a non- constant harmonic function of finite energy then it is not Liouville [9], but the converse is in general not true. Russ Lyons asked ...
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An Alternative Approach to Counting Minimum (s; t)-cuts in Planar Graphs
... simple planar graphs, as the number of edges in a simple planar graph is bounded by a constant multiple of |V | ...simple graphs, and allows for counting minimum cuts in multigraphs, any ...
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Separators in High-Genus Near-Planar Graphs
... of graphs with interesting structure is high-genus near-planar ...These graphs have a high genus, where the number of crossings would be ω(1), ...these graphs are not able to be embedded in a ...
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The Complexity of the Hajós Calculus for Planar Graphs
... planar graphs or PHC is not necessarily complete. In fact there is no obvious extension of the proof for the HC’s completeness to the proof for the PHC’s completeness. Fortunately, however, the proof of our ...
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A Linear Algorithm for Resource Tripartitioning Triconnected Planar Graphs
... But there exists no polynomial-time algorithm for resource k-partitioning of graphs for k > 3. In this pa- per, we give a linear algorithm for finding a resource tripartition of a 3-connected planar graph ...
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NEW CONCEPT OF FUZZY PLANAR GRAPHS
... the graphs are simply models of ...fuzzy graphs was given by Kaufman, ...fuzzy graphs during the same ...fuzzy graphs and give some operations on ...fuzzy graphs. The concept of fuzzy ...
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A New Approach for Vertex Guarding of Planar Graphs
... In the paper, at first, known algorithms are considered, and then a new algorithm working on planar graphs is introduced. The new algorithm is based on the dynamic approach and produces better and faster ...
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{2, 2}-Extendability of Planar Graphs
... all planar graphs are {1,2}- extendable, see Figures ...all planar graphs are {2, 2, 2}-extendable, see Figures ...the graphs in Figures ...of planar graphs which are not ...
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Hyperbolicity vs amenability for planar graphs
... for planar graphs that do not necessarily have many symmetries: we show that these properties become equivalent when strengthened by certain additional conditions, but not ...
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Subcritical graph classes containing all planar graphs
... of planar graphs was actually used: we only used the fact that it is minor-closed (in the proof of Proposition 2), and that its exponential generating function has a non-zero radius of convergence (in the ...
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Regular Augmentations of Planar Graphs with Low Degree
... If we seek the actual augmentation, we first have to find all cycles and the number of vertices it consists of. This can be done by using depth-first-search on the graph. Depth- first-search on a graph G = (V, E) has a ...
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A characterization of graph properties testable for general planar graphs with one sided error (it's all about forbidden subgraphs)
... of graphs, we do it via introducing hyperedges, to ensure that after contracting high degree vertices the information about their neighbors is memorized in a form of a ...from graphs to hypergraphs makes ...
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Improved guarantees for Vertex Sparsification in planar graphs
... The results for reachability-preserving minors are obtained by exploiting the technique of Coppersmith and Elkin [13] on counting “branching” events between shortest paths in the directed setting (this technique has also ...
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Approximate Inference on Planar Graphs using Loop Calculus and Belief Propagation
... We have presented an approximate algorithm based on the exact loop calculus framework for in- ference on planar graphical models defined in terms of binary variables. The proposed approach improves the estimate ...
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PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS
... require graphs that can be decomposed in some way to two planar ...biplanar graphs model electric circuits which require the use of at most two sides of a circuit ...the planar model in Figure ...
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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 face routing ...
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CYCLE SUPER MAGIC LABELING OF PLANAR GRAPHS
... ψ(e) is constant. Moreover G is said to be H-supermagic, if ψ(V (G)) = {1, 2, 3, . . . , |V (G)|}. In this paper, we study the cycle-supermagic labeling of a pumpkin graph and two classes of planar maps containing ...
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Quartic planar graphs
... our graphs are assumed to be finite, undirected, and unless otherwise indicated may have loops and parallel ...our graphs are connected unless otherwise ...
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Planar Graphs. Complement to Chapter 2, The Villas of the Bellevue
... not planar, but this is not always the ...is planar, then 3(V-2) E ...be planar, but it isn’t, because it is impossible to draw it while avoiding all crossovers between ...
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Conflict-Free Vertex Coloring Of Planar Graphs
... It is wasteful to spend time coloring a graph that cannot be conflict-free colored. This leads Abel et al. to provide suf- ficient criterion to guarantee the conflict-free k-colorability of a certain graphs. To ...
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