2022-01-22 02:02:09 +0200 received badge ● Notable Question (source) 2022-01-22 02:02:09 +0200 received badge ● Popular Question (source) 2020-07-01 20:11:40 +0200 commented answer Adding edges to a graph wow this exactly anticipates what I was going to do next, thanks so much for the thorough answer! 2020-07-01 20:11:38 +0200 received badge ● Scholar (source) 2020-07-01 19:00:16 +0200 received badge ● Supporter (source) 2020-07-01 17:49:21 +0200 received badge ● Student (source) 2020-06-30 22:23:58 +0200 asked a question adding an edge to a graph This is my first time using this forum so please let me know if more information is needed I am trying to some basic conjecture testing, so I'm not too concerned about runtime. I am trying to count graphs which are "maximal triangle-free and 3-colorable", ie triangle-free and 3-colorable, and adding any missing edge breaks one of those 2 properties. But I don't know how to test that property about adding edges to a graph, since I don't know how to add edges to a graph. I'm mainly using the Sage page on undirected graphs. My rudimentary code so far is below: n = 5 list = [] for i in range(1,n): list.append([]) for g in graphs(i): if g.is_triangle_free() and g.chromatic_number() <= 3: list[i-1].append(g) list 2020-06-30 22:23:58 +0200 asked a question Adding edges to a graph This is my first time using this forum so please let me know if more information is needed I am trying to some basic conjecture testing, so I'm not too concerned about runtime. I am trying to count graphs which are "maximal triangle-free and 3-colorable", ie triangle-free and 3-colorable, and adding any missing edge breaks one of those 2 properties. But I don't know how to test that property about adding edges to a graph, since I don't know how to add edges to a graph. I'm mainly using the Sage page on undirected graphs. My rudimentary code so far is below: > n = 5 > list = [] > for i in range(1, n): > list.append([]) > for g in graphs(i): > if g.is_triangle_free() and g.chromatic_number() <= 3: > list[i-1].append(g)  list