Be G a graph and let's assume that for every sub graph G^'=(V^',E^' ) |E^' |≤2|V^' |. Show you can direct the graph edges so every exit is at most 2.
57471
Directing graph such that any outdegree would be at most 2
139657
Prove that if $\chi(G-u-v)=\chi(G)-2$ for every vertices $u, v$ ($u \ne v$) then G is complete graph.
122998
number of edges induction proof
87760
Determine the diameter of a graph of order $n \geq 3$ where $\delta (G) \geq \frac{n-1}{2}$.
91134
In any finite graph with at least two vertices, there must be two vertices with the same degree
37984
Prove a planar graph with all regions having even degree can be colored with 2 colors
127965
Graph theory (Graph Connectivity)
79091
Please guide me to draw this : graph of $x \geq 5$ and $y \geq 5$
131736
Proving a triangle with different edge colors exists in a graph.
100978
If a graph with $n$ vertices and $n$ edges there must a cycle?
140444
Prove $\chi(G)\chi(\bar{G}) \geq n$ for chromatic number of graph and its complement
85541
What is the maximum length of a circuit in the complete graph on n vertices.
97630
A graph which is not a single block has at least two leaf blocks
46309
Prove that this graph is nonplanar
158856
Prove that a graph with the same number of edges and vertices contains one cycle
51002
Regular graph (Homework)
142917
Graph vertex chromatic number in a union of 2 sub-graphs