Olaru and Sachs showed the α-perfection of the graphs in which every cycle of length five or more has a pair of crossing diagonals (Sachs 1970, Theorem 5). By Lovász (1972), α-perfection is an equivalent form of definition of perfect graphs. Sachs, Horst (1970), "On the Berge conjecture concerning perfect graphs", Combinatorial Structures and their Applications (Proc. Calgary Internat. Conf., Calgary, Alta., 1969), Gordon and Breach, pp. 377–384, MR0272668. Lovász, László (1972), "Normal hypergraphs and the perfect graph conjecture", Discrete Mathematics, 2 (3): 253–267, doi:10.1016/0012-365X(72)90006-4, MR0302480.
Howorka (1977). Howorka, Edward (1977), "A characterization of distance-hereditary graphs", The Quarterly Journal of Mathematics, Second Series, 28 (112): 417–420, doi:10.1093/qmath/28.4.417, MR0485544.
Cogis & Thierry (2005) present a simple direct algorithm for maximum weighted independent sets in distance-hereditary graphs, based on parsing the graph into pendant vertices and twins, correcting a previous attempt at such an algorithm by Hammer & Maffray (1990). Because distance-hereditary graphs are perfectly orderable, they can be optimally colored in linear time by using LexBFS to find a perfect ordering and then applying a greedy coloring algorithm. Cogis, O.; Thierry, E. (2005), "Computing maximum stable sets for distance-hereditary graphs", Discrete Optimization, 2 (2): 185–188, doi:10.1016/j.disopt.2005.03.004, MR2155518. Hammer, Peter Ladislaw; Maffray, Frédéric (1990), "Completely separable graphs", Discrete Applied Mathematics, 27 (1–2): 85–99, doi:10.1016/0166-218X(90)90131-U, MR1055593.
Olaru and Sachs showed the α-perfection of the graphs in which every cycle of length five or more has a pair of crossing diagonals (Sachs 1970, Theorem 5). By Lovász (1972), α-perfection is an equivalent form of definition of perfect graphs. Sachs, Horst (1970), "On the Berge conjecture concerning perfect graphs", Combinatorial Structures and their Applications (Proc. Calgary Internat. Conf., Calgary, Alta., 1969), Gordon and Breach, pp. 377–384, MR0272668. Lovász, László (1972), "Normal hypergraphs and the perfect graph conjecture", Discrete Mathematics, 2 (3): 253–267, doi:10.1016/0012-365X(72)90006-4, MR0302480.
Howorka (1977). Howorka, Edward (1977), "A characterization of distance-hereditary graphs", The Quarterly Journal of Mathematics, Second Series, 28 (112): 417–420, doi:10.1093/qmath/28.4.417, MR0485544.
Cogis & Thierry (2005) present a simple direct algorithm for maximum weighted independent sets in distance-hereditary graphs, based on parsing the graph into pendant vertices and twins, correcting a previous attempt at such an algorithm by Hammer & Maffray (1990). Because distance-hereditary graphs are perfectly orderable, they can be optimally colored in linear time by using LexBFS to find a perfect ordering and then applying a greedy coloring algorithm. Cogis, O.; Thierry, E. (2005), "Computing maximum stable sets for distance-hereditary graphs", Discrete Optimization, 2 (2): 185–188, doi:10.1016/j.disopt.2005.03.004, MR2155518. Hammer, Peter Ladislaw; Maffray, Frédéric (1990), "Completely separable graphs", Discrete Applied Mathematics, 27 (1–2): 85–99, doi:10.1016/0166-218X(90)90131-U, MR1055593.