Question

Prove that if a graph $G$ has a Hamilton path, then for every $S\subseteq V(G)$, the number of components of $G-S$ is at most $|S|+1$.

score 722 · Answer 1 · 2026-03-25 12:29:25

722

Views

Prove that if a graph $G$ has a Hamilton path, then for every $S\subseteq V(G)$, the number of components of $G-S$ is at most $|S|+1$.

Published on 25 Mar 2026 - 12:29

score 109 · Answer 2 · 2019-02-05 07:26:57

109

Views

meaning of graph embedding

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score 256 · Answer 3 · 2026-03-25 06:17:39

256

Views

Past exam question: probabilistic method

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score 640 · Answer 4 · 2026-03-25 09:48:18

640

Views

Generating the $n^{th}$ full binary tree over $N$ labeled leaves

Published on 25 Mar 2026 - 9:48

score 203 · Answer 5 · 2019-02-05 21:18:21

203

Views

Find (if there exists) a graph $G$ such that $X'(G)=5$ and $X(G)=6$. If there is no such a graph then explain why.

Published on 05 Feb 2019 - 21:18

score 82 · Answer 6 · 2026-03-25 07:46:28

82

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 25 Mar 2026 - 7:46

score 374 · Answer 7 · 2026-04-05 16:29:09

374

Views

Optimization problem for routes

Published on 05 Apr 2026 - 16:29

score 69 · Answer 8 · 2019-02-06 03:51:28

69

Views

Prove that $\bar{G}$ contains a triangle

Published on 06 Feb 2019 - 3:51

score 38 · Answer 9 · 2019-02-06 05:51:51

38

Views

Infinite vertex transitive graphs with bounded simple loops

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score 200 · Answer 10 · 2019-02-06 08:16:54

200

Views

Inductively defined sequence of graph neighborhoods

Published on 06 Feb 2019 - 8:16

score 60 · Answer 11 · 2026-03-30 13:54:26

60

Views

Most common naming for graph edges ("to $\to$ from" vs "in $\to$ out" vs "source $\to$ target", etc)

Published on 30 Mar 2026 - 13:54

score 268 · Answer 12 · 2026-03-25 09:22:40

268

Views

Relation between maximum matching of a graph and its complement

Published on 25 Mar 2026 - 9:22

score 45 · Answer 13 · 2019-02-06 21:43:55

45

Views

how can I visualize such graph and how can I prove it is the way

Published on 06 Feb 2019 - 21:43

score 36 · Answer 14 · 2019-02-06 23:52:45

36

Views

A sequence with the property that it can be be split into n pieces where each piece sums to x, and no other such split exists

Published on 06 Feb 2019 - 23:52

score 43 · Answer 15 · 2026-03-26 09:15:02

43

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Directed Trees Question Help

Published on 26 Mar 2026 - 9:15

List Question

Prove that if a graph $G$ has a Hamilton path, then for every $S\subseteq V(G)$, the number of components of $G-S$ is at most $|S|+1$.

meaning of graph embedding

Past exam question: probabilistic method

Generating the $n^{th}$ full binary tree over $N$ labeled leaves

Find (if there exists) a graph $G$ such that $X'(G)=5$ and $X(G)=6$. If there is no such a graph then explain why.

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

Optimization problem for routes

Prove that $\bar{G}$ contains a triangle

Infinite vertex transitive graphs with bounded simple loops

Inductively defined sequence of graph neighborhoods

Most common naming for graph edges ("to $\to$ from" vs "in $\to$ out" vs "source $\to$ target", etc)

Relation between maximum matching of a graph and its complement

how can I visualize such graph and how can I prove it is the way

A sequence with the property that it can be be split into n pieces where each piece sums to x, and no other such split exists

Directed Trees Question Help

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