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triangle-free graph

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  • Triangle-free graph — In the mathematical area of graph theory, a triangle free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle free graphs may be equivalently defined as graphs with clique number ≤ 2, graphs with girth ≥ 4,… …   Wikipedia

  • Claw-free graph — A claw In graph theory, an area of mathematics, a claw free graph is a graph that does not have a claw as an induced subgraph. A claw is another name for the complete bipartite graph K1,3 (that is, a star graph with three edges, three leaves, and …   Wikipedia

  • Graph coloring — A proper vertex coloring of the Petersen graph with 3 colors, the minimum number possible. In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called colors to elements of a graph… …   Wikipedia

  • Median graph — The median of three vertices in a median graph In mathematics, and more specifically graph theory, a median graph is an undirected graph in which any three vertices a, b, and c have a unique median: a vertex m(a,b,c) that belongs to shortest… …   Wikipedia

  • Grötzsch graph — infobox graph name = Grötzsch graph namesake = Herbert Grötzsch vertices = 11 edges = 20 chromatic number = 4 chromatic index = girth = 4 properties = The Grötzsch graph is a triangle free graph with 11 vertices, 20 edges, and chromatic number 4 …   Wikipedia

  • Chvátal graph — Named after Václav Chvátal Vertices 12 Edges 24 …   Wikipedia

  • Clebsch graph — Named after Alfred Clebsch Vertices 16 Edges 40 …   Wikipedia

  • Intersection number (graph theory) — In the mathematical field of graph theory, the intersection number of a graph is the smallest number of elements in a representation of G as an intersection graph of finite sets. Equivalently, it is the smallest number of cliques needed to cover… …   Wikipedia

  • Outerplanar graph — A maximal outerplanar graph and its 3 coloring. In graph theory, an undirected graph is an outerplanar graph if it can be drawn in the plane without crossings in such a way that all of the vertices belong to the unbounded face of the drawing.… …   Wikipedia

  • Complement graph — The Petersen graph (on the left) and its complement graph (on the right). In graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two vertices of H are adjacent if and only if they are not adjacent in G …   Wikipedia

  • Clique (graph theory) — A graph with 23 1 vertex cliques (its vertices), 42 2 vertex cliques (its edges), 19 3 vertex cliques (the light blue triangles), and 2 4 vertex cliques (dark blue). Six of the edges and 11 of the triangles form maximal cliques. The two dark blue …   Wikipedia

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