Question

Prove that a $d$-regular, $d$-edge-connected graph $G$ is tough when $d\geq3$.

score 109 · Answer 1 · 2018-11-10 18:07:32

109

Views

Prove that a $d$-regular, $d$-edge-connected graph $G$ is tough when $d\geq3$.

Published on 10 Nov 2018 - 18:07

score 407 · Answer 2 · 2026-03-20 08:13:32

407

Views

The subgraph induced by the neighbourhood of a vertex

Published on 20 Mar 2026 - 8:13

score 394 · Answer 3 · 2018-11-18 14:03:22

394

Views

How to verify that a problem is in co-NP or NP?

Published on 18 Nov 2018 - 14:03

score 3.2k · Answer 4 · 2018-11-19 19:57:34

3.2k

Views

Show any two edges in a 2-connected graph lie on a cycle

Published on 19 Nov 2018 - 19:57

score 197 · Answer 5 · 2018-11-22 12:36:13

197

Views

Confusion about the proof of Menger's Theorem in "Introduction to Graph Theory" by Douglas West

Published on 22 Nov 2018 - 12:36

score 533 · Answer 6 · 2018-12-04 22:53:59

533

Views

What is the maximum connectivity of a planar graph?

Published on 04 Dec 2018 - 22:53

score 576 · Answer 7 · 2018-12-05 12:23:02

576

Views

A connected maximal graph $G$ with no cycles of length at least $k+1$ has $|V(G)| \leq k$ or has a cut-vertex when $k \geq 2$

Published on 05 Dec 2018 - 12:23

score 81 · Answer 8 · 2018-12-06 21:14:39

81

Views

What are graph algorithms that benefit (in their time complexity) from using the Adjacency Matrix?

Published on 06 Dec 2018 - 21:14

score 340 · Answer 9 · 2019-02-04 10:25:13

340

Views

Is every $f(k)$-vertex-connected graph the edge-disjoint union of two $k$-vertex-connected graphs?

Published on 04 Feb 2019 - 10:25

score 81 · Answer 10 · 2019-02-05 22:28:43

81

Views

Show that if $|G| \geq 5$ and for each pair of vertices $u,v$ there is an $u−v$ Hamilton path then $\kappa(G) \geq 3$

Published on 05 Feb 2019 - 22:28

score 346 · Answer 11 · 2019-02-14 13:48:29

346

Views

proving that graph G is a path

Published on 14 Feb 2019 - 13:48

score 223 · Answer 12 · 2019-03-03 19:01:25

223

Views

Explicit construction and proving or disproving expander graph for this family

Published on 03 Mar 2019 - 19:01

score 2.3k · Answer 13 · 2019-03-07 06:56:35

2.3k

Views

Show that if $G$ is connected then $L(G)$ is connected

Published on 07 Mar 2019 - 6:56

score 46.1k · Answer 14 · 2019-03-09 19:20:37

46.1k

Views

Are these two graphs isomorphic? Why/Why not?

Published on 09 Mar 2019 - 19:20

score 159 · Answer 15 · 2019-03-13 05:40:08

159

Views

Strengthening of Menger's Theorem

Published on 13 Mar 2019 - 5:40

List Question

Prove that a $d$-regular, $d$-edge-connected graph $G$ is tough when $d\geq3$.

The subgraph induced by the neighbourhood of a vertex

How to verify that a problem is in co-NP or NP?

Show any two edges in a 2-connected graph lie on a cycle

Confusion about the proof of Menger's Theorem in "Introduction to Graph Theory" by Douglas West

What is the maximum connectivity of a planar graph?

A connected maximal graph $G$ with no cycles of length at least $k+1$ has $|V(G)| \leq k$ or has a cut-vertex when $k \geq 2$

What are graph algorithms that benefit (in their time complexity) from using the Adjacency Matrix?

Is every $f(k)$-vertex-connected graph the edge-disjoint union of two $k$-vertex-connected graphs?

Show that if $|G| \geq 5$ and for each pair of vertices $u,v$ there is an $u−v$ Hamilton path then $\kappa(G) \geq 3$

proving that graph G is a path

Explicit construction and proving or disproving expander graph for this family

Show that if $G$ is connected then $L(G)$ is connected

Are these two graphs isomorphic? Why/Why not?

Strengthening of Menger's Theorem

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