Question

Let $n = 4k$ or $n = 4k+1$ for non-negative $k$. Prove that there exist a self-complementary graph $G = (V, E)$, where $|V| =n$

score 344 · Answer 1 · 2026-04-15 18:21:29

344

Views

Let $n = 4k$ or $n = 4k+1$ for non-negative $k$. Prove that there exist a self-complementary graph $G = (V, E)$, where $|V| =n$

Published on 15 Apr 2026 - 18:21

score 134 · Answer 2 · 2026-04-17 10:34:31

134

Views

For any graph there is at least a path of length m/n or longer

Published on 17 Apr 2026 - 10:34

score 43 · Answer 3 · 2026-03-28 01:08:33

43

Views

Draw a tree with $4$ vertices of grade $5$, $8$ of grade $4$, $6$ of grade $3$, $10$ of grade $2$ and $36$ of grade $1$

Published on 28 Mar 2026 - 1:08

score 227 · Answer 4 · 2026-04-11 19:25:45

227

Views

Bipartite graphs not hamiltonian-connected

Published on 11 Apr 2026 - 19:25

score 163 · Answer 5 · 2026-04-14 15:39:59

163

Views

What is the relationship between graph homeomorphism and topology homeomophism？

Published on 14 Apr 2026 - 15:39

score 97 · Answer 6 · 2026-05-10 18:32:43

97

Views

Path counts in a graph via enumerating independent sets of a graphic matroid

Published on 10 May 2026 - 18:32

score 225 · Answer 7 · 2026-04-15 08:11:11

225

Views

Any 2 vertices in G are connected by at least two edge-disjoint paths

Published on 15 Apr 2026 - 8:11

score 159 · Answer 8 · 2026-04-13 07:22:11

159

Views

Random coloring of a grid with no more than two straight nodes the same color, guaranteed to terminate

Published on 13 Apr 2026 - 7:22

score 236 · Answer 9 · 2026-04-15 10:43:21

236

Views

Maximum number of edges in a graph

Published on 15 Apr 2026 - 10:43

score 49 · Answer 10 · 2026-04-15 17:30:51

Let $\text{rad}(G) = r$ and $\text{diam}(G)=d.$ Show that for each $k$ with $r\leq k \leq d,$ there exists $w \in G$ such that $e(w)=k.$

score 144 · Answer 11 · 2026-04-15 22:16:19

144

Views

Solve a recurrence that has two forms for $n$ even or odd

Published on 15 Apr 2026 - 22:16

score 466 · Answer 12 · 2026-04-12 18:18:00

466

Views

Maximum egdes of a cactus graph

Published on 12 Apr 2026 - 18:18

score 2.2k · Answer 13 · 2026-04-13 18:17:14

2.2k

Views

Is a loop (in graph theory) considered adjacent to itself?

Published on 13 Apr 2026 - 18:17

score 481 · Answer 14 · 2026-05-10 14:39:56

481

Views

If all subgraphs of two graphs are pairwise isomorphic, are the graphs themselves isomorphic?

Published on 10 May 2026 - 14:39

score 275 · Answer 15 · 2026-04-14 05:09:29

275

Views

If a graph G contains subdivision of H as graphs then H is a minor

Published on 14 Apr 2026 - 5:09

List Question

Let $n = 4k$ or $n = 4k+1$ for non-negative $k$. Prove that there exist a self-complementary graph $G = (V, E)$, where $|V| =n$

For any graph there is at least a path of length m/n or longer

Draw a tree with $4$ vertices of grade $5$, $8$ of grade $4$, $6$ of grade $3$, $10$ of grade $2$ and $36$ of grade $1$

Bipartite graphs not hamiltonian-connected

What is the relationship between graph homeomorphism and topology homeomophism？

Path counts in a graph via enumerating independent sets of a graphic matroid

Any 2 vertices in G are connected by at least two edge-disjoint paths

Random coloring of a grid with no more than two straight nodes the same color, guaranteed to terminate

Maximum number of edges in a graph

Let $\text{rad}(G) = r$ and $\text{diam}(G)=d.$ Show that for each $k$ with $r\leq k \leq d,$ there exists $w \in G$ such that $e(w)=k.$

Solve a recurrence that has two forms for $n$ even or odd

Maximum egdes of a cactus graph

Is a loop (in graph theory) considered adjacent to itself?

If all subgraphs of two graphs are pairwise isomorphic, are the graphs themselves isomorphic?

If a graph G contains subdivision of H as graphs then H is a minor

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