Question

Prove that if $D$ is a digraph such that $od(v) \geq k \geq 1$ for every $v \in V(D)$ then $D$ contain a cycle of length at least $k+1$

score 935 · Answer 1 · 2026-04-14 00:31:00

Prove that if $D$ is a digraph such that $od(v) \geq k \geq 1$ for every $v \in V(D)$ then $D$ contain a cycle of length at least $k+1$

score 5.5k · Answer 2 · 2026-04-15 06:44:54

5.5k

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178

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1.1k

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196

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score 1.9k · Answer 15 · 2026-04-15 09:51:16

1.9k

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List Question

Prove that if $D$ is a digraph such that $od(v) \geq k \geq 1$ for every $v \in V(D)$ then $D$ contain a cycle of length at least $k+1$

Cycles and faces in planar graphs

Is there a graph with these properties?

For every vertex of a Graph G, k(G-v) = k(G) or k(G-v) = k(g) -1?

Question about the proof of Ramsey's Theorem

number of vertices a special graph

Prove that there is an orientation of $G$ in which no directed path has length $2$ if and only if $g$ is bipartite.

Round table arrrangement for 13 people using graph theory

Convex planar graphs

How would I find a minimum weight spanning tree for W?

Shortest route with a requirements set

Dimension of the cycle/bond space in graph theory

Algorithm producing a minimum spanning tree?

Selecting one number from each set with minimum variance

A bipartite graph and an ordering of its vertices where the greedy algorithm uses at least $2014$ colours

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