sanskarfc

# Trivially perfect graphs are the graphs that do not have a P4 path graph or a C4 cycle graph as induced subgraphs.
# Reference:  Brandstädt, Le & Spinrad (1999), theorem 6.6.1, p. 99; Golumbic (1978), theorem 2. Wolk (1962) and Wolk (1965) proved this for comparability graphs of rooted forests.

# Error: By mistake used DiGraphs here instead of undirected.

# returns true if C4 is present
def checkC4(graph):
    for vertex in graph:
        if(graph.degree(vertex) != 2):
            return False

sanskarfc

# Function to find all minimal separators of a graph
def find_minimal_separators(G):
    separators = []
    visited_separators = {}
    
    # Initial iteration
    for v in G.vertices():           
        N_v = set(G.neighbors(v))
        S = N_v.union({v})
        G_S = G.copy()