ON DIAMETERS A!ND RADII OF BRlDGED GRAPHS
نویسندگان
چکیده
A graph (I’ is bridged if it contains no isometric cycles of length greater than 3. For each positive integer p, let Tp be the graph obtained by triangulating an equilateral triangIe of side p with equilateral triangles of side 1. It is shown that the radius and diameter of a bridged graph containing no isometric TP satisfy the inequality 6r s 3d +p + 3. Thus, for each 8xed p, the radius of a bridged graph containing no isometric TP is within a constant of its theoretical lower bound. Also, letting p = d + 1, it follows that the radius and diameter of an arbitrary bridged graph satisfy the inequality 3r s 2d + 2. The graphs TP, p 2 1, show that this bound on the &ius is best possible. Two results of Chang and Nemhauser concerning diameters and radii of chordal graphs are also corollaries.
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