Equilibrium Small Circuit Double Covers of Near-Triangulations

Abstract:

      A near-triangulation is such a connected planar graph whose inner faces are all triangles but the outer face may be not. Let G be a near-triangulation of order n and C be an SCDC (small circuit double cover)[2] of G. Let (?) Then, C₀ is said to he an equilibrium SCDC of G. In this paper, we show that if G is an outer planar graph, δ(C₀)≤2, otherwiseδ(C₀) ≤4.