A De Bruijn–Erdős Theorem for Chordal Graphs
Copyright policy )A De Bruijn–Erdős Theorem for Chordal Graphs
A special case of a combinatorial theorem of De Bruijn and Erdős asserts that every noncollinear set of $n$ points in the plane determines at least $n$ distinct lines. Chen and Chávtal suggested a possible generalization of this assertion in metric spaces with appropriately defined lines. We prove this generalization in all metric spaces induced by connected chordal graphs.
Distance in graphs, Combinatorial geometries and geometric closure systems, Extremal set theory, 05C99, 05D99, 51G99, [MATH] Mathematics [math], Erdős problems and related topics of discrete geometry, Other designs, configurations, connected chordal graphs, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
Distance in graphs, Combinatorial geometries and geometric closure systems, Extremal set theory, 05C99, 05D99, 51G99, [MATH] Mathematics [math], Erdős problems and related topics of discrete geometry, Other designs, configurations, connected chordal graphs, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
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