Show that a connected simple graph for which every edge is in some perfect matching is a block
35092
Match covered graph is 2-connected
61816
Cut points and connected space
55944
Chromatic polynomial of connected graph $ \leq x(x-1)^{n-1}$
35418
Equivalent definitions for simple connectivity
78110
A connected k-regular bipartite graph is 2-connected.
117707
d-regular bipartite graph
33603
How to get all Perfect or Near-Perfect Matchings of a graph
7626
Proving that every connected graph has a vertex whose removal will not disconnect the graph.
13121
Does every connected $r$-regular bipartite graph contain a Hamiltonian cycle?
99781
Proof that any simple connected graph has at least 2 non-cut vertices.
127965
Graph theory (Graph Connectivity)
20544
Proving that if $G$ has a Hamiltonian circuit, then the line graph $L(G)$ also has a Hamiltonian Circuit
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.
124666
Hamiltonian and non-Hamiltonian connected graph using the same degree sequence
126428
Prove the edges of a multigraph may be oriented such that the net-degree of any vertex is $\leq 1$.
49703
Analogue of closed graph theorem
108417
Cycles of length k in a complete simple graph with n vertices