03918391

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03918391 Quilliot, Alain On the Helly property working as a compactness criterion on graphs. J. Comb. Theory, Ser. A 40, 186-193 (1985). 1985 Elsevier Science (Academic Press), San Diego, CA EN connected graph automorphism group Helly graph fixed point theorem

doi:10.1016/0097-3165(85)90061-5

Given a connected graph (X,E), denote by $d\sb G$ the distance given by the graph. Let ${\cal E}$ be a family of all balls, i.e. sets $\{$ $y\in X;d\sb G(x,y)\le p\}$, $x\in X$, $p\in N$. Then (X,E) is a Helly graph provided every subfamily of ${\cal E}$ in which every pair of balls meets has a non-trivial intersection. The automorphism group of a finite Helly graph is studied and fixed point theorem for finite Helly graphs is proved. M.Demlov\'a