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  2. Shannon switching game - Wikipedia

    en.wikipedia.org/wiki/Shannon_switching_game

    The game is played on a finite graph with two special nodes, A and B. Each edge of the graph can be either colored or removed. The two players are called Short and Cut, and alternate moves. On Cut's turn, Cut deletes from the graph a non-colored edge of their choice. On Short's turn, Short colors any edge still in the graph.

  3. SPQR tree - Wikipedia

    en.wikipedia.org/wiki/SPQR_tree

    Each edge in a graph G x may be a virtual edge for at most one SPQR tree edge. An SPQR tree T represents a 2-connected graph G T , formed as follows. Whenever SPQR tree edge xy associates the virtual edge ab of G x with the virtual edge cd of G y , form a single larger graph by merging a and c into a single supervertex, merging b and d into ...

  4. Graph theory - Wikipedia

    en.wikipedia.org/wiki/Graph_theory

    A directed graph with three vertices and four directed edges (the double arrow represents an edge in each direction). A directed graph or digraph is a graph in which edges have orientations. In one restricted but very common sense of the term, [5] a directed graph is an ordered pair = (,) comprising:

  5. Hypergraph - Wikipedia

    en.wikipedia.org/wiki/Hypergraph

    In particular, there is a bipartite "incidence graph" or "Levi graph" corresponding to every hypergraph, and conversely, every bipartite graph can be regarded as the incidence graph of a hypergraph when it is 2-colored and it is indicated which color class corresponds to hypergraph vertices and which to hypergraph edges.

  6. Boundary (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Boundary_(graph_theory)

    The edge boundary is the set of edges with one endpoint in the inner boundary and one endpoint in the outer boundary. [ 1 ] These boundaries and their sizes are particularly relevant for isoperimetric problems in graphs , separator theorems , minimum cuts , expander graphs , and percolation theory .

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    mail.aol.com

    Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!

  8. Edge coloring - Wikipedia

    en.wikipedia.org/wiki/Edge_coloring

    It is straightforward to test whether a graph may be edge colored with one or two colors, so the first nontrivial case of edge coloring is testing whether a graph has a 3-edge-coloring. As Kowalik (2009) showed, it is possible to test whether a graph has a 3-edge-coloring in time O(1.344 n), while using only polynomial space. Although this time ...

  9. Train track map - Wikipedia

    en.wikipedia.org/wiki/Train_track_map

    Let φ be the automorphism of F(a,b) given by φ(a) = b, φ(b) = ab. Let Γ be the wedge of two loop-edges E a and E b corresponding to the free basis elements a and b, wedged at the vertex v. Let f : Γ → Γ be the map which fixes v and sends the edge E a to E b and that sends the edge E b to the edge-path E a E b.