KöMaL 2026 B5509

Let $V=\{v_1,v_2,\ldots,v_n\}$ be the set of vertices of a graph on $n$ vertices, and let $d_i$ denote the degree of vertex $v_i$. We call function $f$ Verőcese , if it takes non-negative real values and for every edge $v_iv_j$ of the graph $f(v_i)+f(v_j)\geq d_i+d_j$ holds. Find the largest real number $\lambda$ such that for every $n$, every simple graph on $n$ vertices and every Verőcese function $f$ $f(v_1)+f(v_2)+\ldots+f(v_n)\geq\lambda(d_1+d_2+\ldots+d_n)$ holds true.