Holmgren si laureò presso l'Università dello Utah nel 1936 e conseguì il titolo di M.Sc. presso lo USAC nel 1942. In seguito, fu professore di Botanica presso lo Utah State Agricultural College.
Opere principali Arthur H. Holmgren, Noel H. Holmgren, Euphorbia aaron-rossii (Euphorbiaceae), a new species from Marble and Grand Canyons of the Colorado River, Arizona, Ed. New York Botanical Garden, 1988, 6 pp. Leila M. Shultz, Arthur H. Holmgren, A new species of Townsendia (Asteraceae) from northern Arizona, Ed. New York Botanical Garden, 1980, 4 pp. Some intermountain endemics, Volume 55 della Faculty honor lecture, Ed. Utah State Univ., 1977, 12 pp.
Libri Mountain plants of Northeastern Utah, Volume 506 della serie Utah Cooperative Extension Service HG, Ed. Utah State Univ., 1996, 132 pp. Handbook of the vascular plants of the Northern Wasatch, 4ª ed., Utah State Agricultural college, 1972, 202 pp. Arthur Cronquist, Arthur H. Holmgren, Noel H. Holmgren, James L. Reveal, Intermountain flora: vascular plants of the Intermountain West, U.S.A.: Geological and botanical history of the region, its plant geography and a glossary. The vascular cryptograms and the gymnosperms, Ed. Hafner Pub. Co., 1972, 270 pp. Arthur H. Holmgren, Berniece A. Andersen, Weeds of Utah, Volume 21 dello Special report, Ed. Utah Agricultural Experiment Station, 1971, 115 pp. Berniece A. Andersen, Arthur H. Holmgren, Mountain plants of northeastern Utah, Volume 319 di Extension circular. Ed. Utah State Univ., 1970, 142 pp. Berniece A. Andersen, Arthur H. Holmgren, A beginner's guide to mountain flowers, Volume 355 di Utah Cooperative Extension Service New Circular Series, 1970, 60 pp. Identification key to common western grasses, 1965, 98 pp. The vascular plants of the Dinosaur National Monument, Ed. Utah State Univ, 1962, 42 pp. Portulacaceae of Nevada. Volume 36 di Contributions toward a flora of Nevada, Ed. Plant Industry Station, 1955, 36 pp. Laurence Alexander Stoddart, Arthur H. Holmgren, C. Wayne Cook, 1949. Important poisonous plants of Utah, Volume 2 dello Special report, Ed. Agricultural Experiment Station, Utah State Agricultural College, 21 pp. Arthur H. Holmgren, Bassett Maguire, Noxious weeds of Utah farm lands, Volume 123 di Circular, 1949, 48 pp. Handbook of the vascular plants of northeastern Nevada. Ed. Logan, Utah State Agricultural College & Experiment Station, 1942, 214 pp.
Onorificenze In suo onore sono stati assegnati i seguenti nomi:
Genere (Onagraceae) Holmgrenia W.L.Wagner & HochSyst. Bot. Monogr. 83: 127. 2007; nom. illeg.
Specie (Brassicaceae) Cardamine holmgrenii Al-ShehbazHarvard Pap. Bot. 11(2): 275. enero 2007 (Polygonaceae) Eriogonum holmgrenii RevealLeafl. W. Bot. 10: 184. 1965 (GCI)
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