Question

If $G$ is a planar graph of girth $g$ that is not a forest, then $e(G)\leq g (v(G) − 2)$

score 130 · Answer 1 · 2023-11-04 01:33:19

130

Views

If $G$ is a planar graph of girth $g$ that is not a forest, then $e(G)\leq g (v(G) − 2)$

Published on 04 Nov 2023 - 1:33

score 62 · Answer 2 · 2023-11-05 13:47:59

62

Views

Do there exist 5-reguler planar, 3-connected (4 or 5 connected?) hamiltonian graphs which are not pancyclic?

Published on 05 Nov 2023 - 13:47

score 128 · Answer 3 · 2023-11-16 21:15:59

128

Views

How many trees with $n$ vertices correspond to the vector $(g_1,g_2,g_3,g_4)$, where the $g_i$ are the number of vertices of degree $i$?

Published on 16 Nov 2023 - 21:15

score 26 · Answer 4 · 2023-11-19 06:57:51

26

Views

Corolary of Euler's identity Theorem in planar graphs

Published on 19 Nov 2023 - 6:57

score 49 · Answer 5 · 2026-03-14 10:13:28

49

Views

Can we draw the dual graph with straight lines?

Published on 14 Mar 2026 - 10:13

score 48 · Answer 6 · 2026-03-26 19:16:58

48

Views

Using Euler formula to prove maximum number of lines in planar graph without triangles

Published on 26 Mar 2026 - 19:16

score 25 · Answer 7 · 2026-03-26 19:20:53

25

Views

Bounds on chromatic number in terms of chromatic numbers of subgraphs.

Published on 26 Mar 2026 - 19:20

score 55 · Answer 8 · 2023-12-12 22:01:30

55

Views

In what way is the hypercube graph $Q_4$ non planar?

Published on 12 Dec 2023 - 22:01

score 36 · Answer 9 · 2026-03-26 21:10:13

36

Views

Find the maximum number of edges in a planar subgraph of G

Published on 26 Mar 2026 - 21:10

score 122 · Answer 10 · 2023-12-16 21:03:25

122

Views

Where does my short proof of the 4-colour theorem go amiss?

Published on 16 Dec 2023 - 21:03

score 42 · Answer 11 · 2023-12-27 22:28:31

42

Views

Prove that the complement of a simple embedded graph $G$ is not embeddable on an orientable surface of genus $g$

Published on 27 Dec 2023 - 22:28

score 39 · Answer 12 · 2023-12-28 18:33:22

39

Views

Why can we assume a triangulated graph without loss of generality, for proofs of the 4 colour theorem?

Published on 28 Dec 2023 - 18:33

score 49 · Answer 13 · 2023-12-31 14:48:38

49

Views

All simple planar graphs have a vertex of degree at most $5$ (wheel of $n>5$).

Published on 31 Dec 2023 - 14:48

score 59 · Answer 14 · 2026-03-27 00:00:24

59

Views

Planar graphs and isomorphism

Published on 27 Mar 2026 - 0:00

score 31 · Answer 15 · 2024-01-05 16:36:10

31

Views

planar 4 regular graph

Published on 05 Jan 2024 - 16:36

List Question

If $G$ is a planar graph of girth $g$ that is not a forest, then $e(G)\leq g (v(G) − 2)$

Do there exist 5-reguler planar, 3-connected (4 or 5 connected?) hamiltonian graphs which are not pancyclic?

How many trees with $n$ vertices correspond to the vector $(g_1,g_2,g_3,g_4)$, where the $g_i$ are the number of vertices of degree $i$?

Corolary of Euler's identity Theorem in planar graphs

Can we draw the dual graph with straight lines?

Using Euler formula to prove maximum number of lines in planar graph without triangles

Bounds on chromatic number in terms of chromatic numbers of subgraphs.

In what way is the hypercube graph $Q_4$ non planar?

Find the maximum number of edges in a planar subgraph of G

Where does my short proof of the 4-colour theorem go amiss?

Prove that the complement of a simple embedded graph $G$ is not embeddable on an orientable surface of genus $g$

Why can we assume a triangulated graph without loss of generality, for proofs of the 4 colour theorem?

All simple planar graphs have a vertex of degree at most $5$ (wheel of $n>5$).

Planar graphs and isomorphism

planar 4 regular graph

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