List questions from planar-graphs

Published on 11 Jun 2021 - 3:46

924

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If $G$ is a connected planar graph then with at least three vertices, $e$ edges and $r$ regions, prove that $e \leq 3n - 6$.

Published on 12 Jun 2021 - 15:27

134

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Plane Regular Graph of Pentagons and Hexagons

Published on 13 Jun 2021 - 20:52

55

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graph theory,planar graph

Published on 14 Jun 2021 - 19:21

189

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Give an example of a function $f : R → R$ whose graph is invariant under a $90^{\circ}$ rotation about the origin.

Published on 21 Jun 2021 - 18:06

260

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IGO 2017 P4 of Combinatorial Geometry

Published on 29 Mar 2026 - 4:33

368

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About $K_{3,3}$ being planar or not

Published on 25 Jun 2021 - 20:35

228

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Largest Planar Subgraph of a Bipartite Graph

Published on 27 Mar 2026 - 12:11

103

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Generate a new planar graph via edge subdivision and edge addition

Published on 28 Jun 2021 - 16:19

176

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Weak Duals of Outerplanar Graphs

Published on 03 Jul 2021 - 17:20

165

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Determine whether my graph is planar or not

Published on 05 Jul 2021 - 21:13

291

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Maximum hitting time for random walks on graphs with few edges

Published on 06 Jul 2021 - 7:10

248

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Showing every planar graph on $n$ vertices has a vertex-cover of size at most $\frac{3n}{4}$ and an independent set of size at least $\frac{n}{4}$

Published on 06 Jul 2021 - 21:41

113

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Mac Lane's Planarity Criterion Proof

Published on 15 Jul 2021 - 20:12

87

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Prove that the graph obtained by removing all 3 vertices on the outer face of a triangulating planar graph is connected.

Published on 19 Jul 2021 - 12:17

List Question

Why do they have no convex drawing?

If $G$ is a connected planar graph then with at least three vertices, $e$ edges and $r$ regions, prove that $e \leq 3n - 6$.

Plane Regular Graph of Pentagons and Hexagons

graph theory,planar graph

Give an example of a function $f : R → R$ whose graph is invariant under a $90^{\circ}$ rotation about the origin.

IGO 2017 P4 of Combinatorial Geometry

About $K_{3,3}$ being planar or not

Largest Planar Subgraph of a Bipartite Graph

Generate a new planar graph via edge subdivision and edge addition

Weak Duals of Outerplanar Graphs

Determine whether my graph is planar or not

Maximum hitting time for random walks on graphs with few edges

Showing every planar graph on $n$ vertices has a vertex-cover of size at most $\frac{3n}{4}$ and an independent set of size at least $\frac{n}{4}$

Mac Lane's Planarity Criterion Proof

Prove that the graph obtained by removing all 3 vertices on the outer face of a triangulating planar graph is connected.

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