We introduce a new hereditary class of graphs, the dominant-matching graphs, and we characterize it in terms of forbidden induced subgraphs.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1246, author = {Igor' E. Zverovich and Olga I. Zverovich}, title = {Dominant-matching graphs}, journal = {Discussiones Mathematicae Graph Theory}, volume = {24}, year = {2004}, pages = {485-490}, zbl = {1065.05074}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1246} }
Igor' E. Zverovich; Olga I. Zverovich. Dominant-matching graphs. Discussiones Mathematicae Graph Theory, Tome 24 (2004) pp. 485-490. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1246/
[000] [1] L. Lovász and M. Plummer, Matching Theory, North-Holland Math. Stud. 121, Annals Discrete Math. 29 (North-Holland Publ. Co., Amsterdam-New York; Akad. Kiadó, Budapest, 1986) xxvii+544 pp.
[001] [2] L. Volkmann, On graphs with equal domination and edge independence numbers, Ars Combin. 41 (1995) 45-56. | Zbl 0842.05052
[002] [3] I.E. Zverovich, k-bounded classes of dominant-independent perfect graphs, J. Graph Theory 32 (1999) 303-310, doi: 10.1002/(SICI)1097-0118(199911)32:3<303::AID-JGT8>3.0.CO;2-B | Zbl 0944.05073
[003] [4] I.E. Zverovich, Perfect connected-dominant graphs, Discuss. Math. Graph Theory 23 (2003) 159-162, doi: 10.7151/dmgt.1192. | Zbl 1037.05038
[004] [5] I.E. Zverovich and V.E. Zverovich, A semi-induced subgraph characterization of upper domination perfect graphs, J. Graph Theory 31 (1999) 29-49, doi: 10.1002/(SICI)1097-0118(199905)31:1<29::AID-JGT4>3.0.CO;2-G | Zbl 0920.05060
[005] [6] I.E. Zverovich and V.E. Zverovich, An induced subgraph characterization of domination perfect graphs, J. Graph Theory 20 (1995) 375-395, doi: 10.1002/jgt.3190200313. | Zbl 0836.05067