Smooth tropical complete intersection curves of genus 3 in $$\mathbb {R}^3$$

We develop a method for describing the tropical complete intersection of hypersurface and plane in $$\mathbb {R}^3$$ . This involves determining topological type curve {R}_{\le 0}^2$$ by using polyhedral complex. As an application, we study smooth curves genus 3 In particular, show that there are no whose skeletons lollipop graph 3. gives partial answer to problem Morrison [6].