A result on the optimal binding function of odd signable graphs

Let ${\\cal~G}$ be a family of graphs. We say that ${\\cal~G}$ is a $\\chi$- bounded family if there is a function $f$ such that,for each $G\\in{\\cal~G}$, $\\chi(G)\\le~f(\\omega(G))$, and call $f$ a binding-function of ${\\cal~G}$. In this paper, we study the problem related to the optimal binding function of odd signable graphs, and prove that a subclass of odd signable graphs has the linear binding function.