Prove that there exists a bipartite subgraph containing at least half of the edges in the original graph.
89531
Show that every graph $G$ has a bipartite subgraph with at least half of the edges of $G$
122998
number of edges induction proof
31854
Proof - raising adjacency matrix to $n$-th power gives $n$-length walks between two vertices
147282
Prove that in every graph with at least two vertices, there are at least two vertices which have the same degree?
141529
Proving existence of a minimum
4112
How to prove that a simple graph having 11 or more vertices or its complement is not planar?
60076
A graph $G$ is bipartite if and only if $G$ can be coloured with 2 colours
72417
Bipartite graphs
101520
Let $G$ be a graph of minimum degree $k>1$. Show that $G$ has a cycle of length at least $k+1$
13226
If $n$ is a natural number $\ge 2$ how do I prove that any graph with $n$ vertices has at least two vertices of the same degree?
126428
Prove the edges of a multigraph may be oriented such that the net-degree of any vertex is $\leq 1$.
33316
Show that if $G$ is simple a graph with $n$ vertices and 􏰈the number of edges $m>\binom{n-1}{2}$, then $G$ is connected.
110876
Prove that $p\mid \binom{p}{k},\ 0< k< p$
158856
Prove that a graph with the same number of edges and vertices contains one cycle
142917
Graph vertex chromatic number in a union of 2 sub-graphs
148438
Show that every nontrivial connected graph $G$ has a closed spanning walk that contains every edge of $G$ exactly twice.
140114
Using Halls Theorem to show Graph contains a perfect matching containing any edge.