Perfect graphs

Line perfect graph

In graph theory, a line perfect graph is a graph whose line graph is a perfect graph. Equivalently, these are the graphs in which every odd-length simple cycle is a triangle. A graph is line perfect if and only if each of its biconnected components is a bipartite graph, the complete graph K4, or a triangular book K1,1,n. Because these three types of biconnected component are all perfect graphs themselves, every line perfect graph is itself perfect. By similar reasoning, every line perfect graph is a parity graph, a Meyniel graph, and a perfectly orderable graph. Line perfect graphs generalize the bipartite graphs, and share with them the properties that the maximum matching and minimum vertex cover have the same size, and that the chromatic index equals the maximum degree. (Wikipedia).

Line perfect graph
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Straight line graphs (parallel)

Powered by https://www.numerise.com/ Straight line graphs (parallel)

From playlist Linear sequences & straight lines

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Graph Theory: 57. Planar Graphs

A planar graph is a graph that can be drawn in the plane without any edge crossings. Such a drawing (with no edge crossings) is called a plane graph. A given plane graph divides the plane into regions and each region has a boundary that outlines it. We look at some examples and also giv

From playlist Graph Theory part-10

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Straight line graphs 8

Powered by https://www.numerise.com/ Straight line graphs 8

From playlist Linear sequences & straight lines

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From playlist Graph Theory

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Straight line graphs (alternative way to define)

Powered by https://www.numerise.com/ Straight line graphs (alternative way to define)

From playlist Linear sequences & straight lines

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From playlist Graph Theory

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Graph Theory: 59. Maximal Planar Graphs

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From playlist Graph Theory part-10

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What are Connected Graphs? | Graph Theory

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From playlist Graph Theory

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Straight line graphs 5

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From playlist Linear sequences & straight lines

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From playlist Probability and Statistics

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From playlist Topic 11/21 Measurement and data processing

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riding every amusement park ride in the shortest possible time

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From playlist Summer of Math Exposition 2 videos

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From playlist Mathematics

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From playlist Mathematics

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From playlist Learn R + Statistics

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From playlist Minitab 17 Instructional Videos

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From playlist Graph Theory FAQs

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From playlist Graph Horizontal Parabola (General Form) #Conics

Related pages

Peripheral cycle | Book (graph theory) | Meyniel graph | Graph theory | Graph (discrete mathematics) | Parity graph | Bipartite graph | Perfectly orderable graph | Line graph | Complete graph | Strangulated graph | Biconnected component | Perfect graph