Question

Prove that we can turn a hypercube into a tree by deleting the correct number of edges

score 69 · Answer 1 · 2023-08-14 07:36:24

69

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Prove that we can turn a hypercube into a tree by deleting the correct number of edges

Published on 14 Aug 2023 - 7:36

score 79 · Answer 2 · 2023-09-04 22:50:52

79

Views

2-connected graphs that contain no even cycle have a very simple structure

Published on 04 Sep 2023 - 22:50

score 80 · Answer 3 · 2023-10-07 17:02:03

80

Views

Minimum cost k-edge connected subgraph

Published on 07 Oct 2023 - 17:02

score 72 · Answer 4 · 2023-10-20 22:39:04

72

Views

How to show κ′(G) = δ(G) for δ(G) ≥ ⌊n/2⌋

Published on 20 Oct 2023 - 22:39

score 98 · Answer 5 · 2023-10-22 16:19:21

98

Views

graphs that when removing any path are still connected

Published on 22 Oct 2023 - 16:19

score 85 · Answer 6 · 2023-10-23 09:20:34

85

Views

Which graphs remain connected when any connected subgraph is removed?

Published on 23 Oct 2023 - 9:20

score 56 · Answer 7 · 2023-11-07 18:24:54

56

Views

Determine if each of the following graphs is connected and/or super-connected. Briefly justify your responses.

Published on 07 Nov 2023 - 18:24

score 38 · Answer 8 · 2023-11-14 21:09:28

38

Views

Subdivision of G has same connectivity as G

Published on 14 Nov 2023 - 21:09

score 45 · Answer 9 · 2023-11-16 17:25:46

45

Views

Name of the edge whose removal causes the graph to be weakly connected

Published on 16 Nov 2023 - 17:25

score 57 · Answer 10 · 2023-11-24 02:52:19

57

Views

How to extract a connected tree of nodes from undirected graph with certain attributes?

Published on 24 Nov 2023 - 2:52

score 232 · Answer 11 · 2023-12-03 10:47:53

Graph theory proof - if $G$ is $2$-connected then for each $u$ there exists $v$ and a cycle $C$ that includes $u, v$ and all of $v$'s neighbors

score 457 · Answer 12 · 2023-12-04 01:37:49

457

Views

Let G be a connected graph in which every vertex has degree three. Show that if G has no cut-edge then every two edges of G lie on a common cycle.

Published on 04 Dec 2023 - 1:37

score 65 · Answer 13 · 2023-12-07 14:47:01

65

Views

If a simple graph $G$ is not connected, then $\overline{G}$ is connected

Published on 07 Dec 2023 - 14:47

score 45 · Answer 14 · 2023-12-09 07:27:22

45

Views

Connectivity of bipartite graph

Published on 09 Dec 2023 - 7:27

score 72 · Answer 15 · 2023-12-15 21:12:31

72

Views

G a k-connected bipartite graph with bipartition $(A, B)$ such that $|A|$, $|B| \geq 2k$. Show that $G$ contains a matching of size $2k$.

Published on 15 Dec 2023 - 21:12

List Question

Prove that we can turn a hypercube into a tree by deleting the correct number of edges

2-connected graphs that contain no even cycle have a very simple structure

Minimum cost k-edge connected subgraph

How to show κ′(G) = δ(G) for δ(G) ≥ ⌊n/2⌋

graphs that when removing any path are still connected

Which graphs remain connected when any connected subgraph is removed?

Determine if each of the following graphs is connected and/or super-connected. Briefly justify your responses.

Subdivision of G has same connectivity as G

Name of the edge whose removal causes the graph to be weakly connected

How to extract a connected tree of nodes from undirected graph with certain attributes?

Graph theory proof - if $G$ is $2$-connected then for each $u$ there exists $v$ and a cycle $C$ that includes $u, v$ and all of $v$'s neighbors

Let G be a connected graph in which every vertex has degree three. Show that if G has no cut-edge then every two edges of G lie on a common cycle.

If a simple graph $G$ is not connected, then $\overline{G}$ is connected

Connectivity of bipartite graph

G a k-connected bipartite graph with bipartition $(A, B)$ such that $|A|$, $|B| \geq 2k$. Show that $G$ contains a matching of size $2k$.

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