Question

Find a necessary and sufficient condition for the Cartesian product $G \times H$ is Eulerian, for $G$ and $H$ are non trivial connected graphs.

score 1.7k · Answer 1 · 2026-04-16 13:59:53

Find a necessary and sufficient condition for the Cartesian product $G \times H$ is Eulerian, for $G$ and $H$ are non trivial connected graphs.

score 1.6k · Answer 2 · 2026-04-17 05:23:30

Prove or disprove if $G$ is 2-edge-connected then there exist 2 edges disjoint $u-v$ trail such that every edge of $G$ lies on one of these trails.

score 893 · Answer 3 · 2026-04-16 10:50:46

893

Views

Prove that an Eulerian graph $G$ has even size iff $G$ has an even number of vertices $V$ which $\deg(v) \equiv 2\pmod 4$

Published on 16 Apr 2026 - 10:50

score 123 · Answer 4 · 2026-04-17 06:11:39

123

Views

Connections between loops (algebraic structure) and graphs

Published on 17 Apr 2026 - 6:11

score 670 · Answer 5 · 2026-04-14 12:13:13

670

Views

Find the minimum capacity edge that is maximized among all paths from $s$ to $t$

Published on 14 Apr 2026 - 12:13

score 1.9k · Answer 6 · 2026-04-13 02:51:24

1.9k

Views

Method for finding bridges and articulation points using DFS

Published on 13 Apr 2026 - 2:51

score 63 · Answer 7 · 2026-04-17 03:28:02

63

Views

Least number $k$ , such there is no graph with $n$ nodes and $k$ hamilton-cycles

Published on 17 Apr 2026 - 3:28

score 859 · Answer 8 · 2026-04-15 21:38:31

859

Views

show that if $T$ is a tree containing at least one vertex of degree $2$ then $\overline T$ is not Eulerian.

Published on 15 Apr 2026 - 21:38

score 681 · Answer 9 · 2026-04-13 16:37:50

681

Views

Soundness of a simple tree edge count proof by induction

Published on 13 Apr 2026 - 16:37

score 177 · Answer 10 · 2026-04-13 19:53:18

177

Views

Spreading a rumour to at least x people with a minimum probability p

Published on 13 Apr 2026 - 19:53

score 127 · Answer 11 · 2026-04-16 10:09:26

127

Views

Graph of all sets

Published on 16 Apr 2026 - 10:09

score 85 · Answer 12 · 2026-04-14 22:33:19

85

Views

Paths of Nearest Neighbours

Published on 14 Apr 2026 - 22:33

score 839 · Answer 13 · 2026-04-12 07:05:25

Is the path between 2 vertices of a Minimum weight tree of a graph the shortest path between those 2 vertices?

score 154 · Answer 14 · 2026-04-12 16:38:11

154

Views

Partition in graph connecting itself and other half

Published on 12 Apr 2026 - 16:38

score 268 · Answer 15 · 2026-04-16 07:02:44

268

Views

Proportion of asymmetric graphs

Published on 16 Apr 2026 - 7:02

List Question

Find a necessary and sufficient condition for the Cartesian product $G \times H$ is Eulerian, for $G$ and $H$ are non trivial connected graphs.

Prove or disprove if $G$ is 2-edge-connected then there exist 2 edges disjoint $u-v$ trail such that every edge of $G$ lies on one of these trails.

Prove that an Eulerian graph $G$ has even size iff $G$ has an even number of vertices $V$ which $\deg(v) \equiv 2\pmod 4$

Connections between loops (algebraic structure) and graphs

Find the minimum capacity edge that is maximized among all paths from $s$ to $t$

Method for finding bridges and articulation points using DFS

Least number $k$ , such there is no graph with $n$ nodes and $k$ hamilton-cycles

show that if $T$ is a tree containing at least one vertex of degree $2$ then $\overline T$ is not Eulerian.

Soundness of a simple tree edge count proof by induction

Spreading a rumour to at least x people with a minimum probability p

Graph of all sets

Paths of Nearest Neighbours

Is the path between 2 vertices of a Minimum weight tree of a graph the shortest path between those 2 vertices?

Partition in graph connecting itself and other half

Proportion of asymmetric graphs

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