Written on the Wall II - Conjecture 160

WOWII Conjecture 160

For a simple connected graph $G$, $L_s(G) \ge \max_v l(v) + \max_v T(v) \cdot c_{C_4}(G)$ where:

• $L_s(G) = \mathrm{SimpleGraph.Ls}\, G$ is the maximum number of leaves over all spanning trees of $G$,
• $\max_v l(v)$ is the maximum local independence number over vertices,
• $\max_v T(v)$ is the maximum number of triangles incident to any vertex,
• $c_{C_4}(G)$ is the number of induced 4-cycles in $G$.