List questions from graph-theory

Published on 10 May 2026 - 22:07

152

Views

Let $T(n,k)$ be the maximum number of vertices with degree $\geq k+1$ for non-root vertices, and $\geq k$ for roots, in a tree with n vertices total.

Published on 15 Apr 2026 - 3:34

170

Views

Given a graph $G$, prove that $m(G) \ge n(G) - c(G) $

Published on 10 May 2026 - 19:35

107

Views

Cat chasing mouse on a straight line coin toss

Published on 15 Apr 2026 - 10:07

37

Views

Forming a graph model

Published on 12 Apr 2026 - 12:04

84

Views

Show that if $G$ is a $k$-regular graph of order $n$, then G has $\frac{nk}{2}$ edges.

Published on 17 Apr 2026 - 0:41

1.3k

Views

Show that every induced subgraph of a bipartite graph is bipartite.

Published on 13 Apr 2026 - 6:48

156

Views

Graph Theory Isomorphism

Published on 11 May 2026 - 8:42

37

Views

Common elements in finite LCM closed sets.

Published on 12 Apr 2026 - 11:10

819

Views

Is it possible to make an infinite directed acyclic graph with all vertices having a indegree of at least one

Published on 14 Apr 2026 - 22:50

108

Views

The name for planar graph where the position of vertices and shape of the edges matter

Published on 26 Mar 2026 - 6:34

29

Views

Show that there exists a single cycle of $G$, noted $C_A (e)$, such that $e$ is the only edge of $C_A (e)$ which is not in $G '$.

Published on 14 Apr 2026 - 15:53

114

Views

Are trees of bounded height well-quasi-ordered by the subgraph relation?

Published on 14 Apr 2026 - 5:18

212

Views

Uniqueness of a minimum capacity $s-t$ cut

Published on 11 May 2026 - 8:29

218

Views

Values of $s-t$ flows and cuts

Published on 14 May 2026 - 8:53

List Question

When a quotient map of topological graph is open?

Let $T(n,k)$ be the maximum number of vertices with degree $\geq k+1$ for non-root vertices, and $\geq k$ for roots, in a tree with n vertices total.

Given a graph $G$, prove that $m(G) \ge n(G) - c(G) $

Cat chasing mouse on a straight line coin toss

Forming a graph model

Show that if $G$ is a $k$-regular graph of order $n$, then G has $\frac{nk}{2}$ edges.

Show that every induced subgraph of a bipartite graph is bipartite.

Graph Theory Isomorphism

Common elements in finite LCM closed sets.

Is it possible to make an infinite directed acyclic graph with all vertices having a indegree of at least one

The name for planar graph where the position of vertices and shape of the edges matter

Show that there exists a single cycle of $G$, noted $C_A (e)$, such that $e$ is the only edge of $C_A (e)$ which is not in $G '$.

Are trees of bounded height well-quasi-ordered by the subgraph relation?

Uniqueness of a minimum capacity $s-t$ cut

Values of $s-t$ flows and cuts

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