Prove that two paths connected from opposite sides of a square must interesect.
44980
Prove that two paths on opposing corners of the unit square must cross.
64504
Prove that the point of intersection of the diagonals of the trapezium lies on the line passing through the mid-points of the parallel sides
69358
Given a simple graph and its complement, prove that either of them is always connected.
116538
Proof of Connected Diagrams
126060
Proving that a Euler Circuit has a even degree for every vertex
59831
How to relate combinatorial proof to bipartite graphs?
92106
Prove that $n$ is a sum of two squares?
128034
Problem on Extremal Graphs: three independent paths
34210
Connecting square vertexes with minimal road
39753
Proving that in a simple graph with $n$ vertices, two vertices have the same degree
57250
Proving that the sum and difference of two squares (not equal to zero) can't both be squares.
39276
Ground Plan - Prove Fermat-Euclid's Totient Theorem with Lagrange's Theorem
49585
Proof a graph is bipartite if and only if it contains no odd cycles
102598
Show that $X$ is path connected if and only if each $X_\alpha$ is path connected.
111032
Proof of Sets involving the Cartesian Product
35458
Prove, that graph $G$ has at least $\chi(G)(\chi(G)-1)/2$ edges.
94570
Proof that every odd integer is a difference of two squares