A graph is called perfect matching compact (briefly, PM-compact), if its perfect matching graph is complete. Matching-covered PM-compact bipartite graphs have been characterized. In this paper, we show that any PM-compact bipartite graph G with δ (G) ≥ 2 has an ear decomposition such that each graph in the decomposition sequence is also PM-compact, which implies that G is matching-covered
@article{bwmeta1.element.doi-10_7151_dmgt_1706, author = {Jinfeng Liu and Xiumei Wang}, title = {A note on pm-compact bipartite graphs}, journal = {Discussiones Mathematicae Graph Theory}, volume = {34}, year = {2014}, pages = {409-413}, zbl = {1290.05121}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1706} }
Jinfeng Liu; Xiumei Wang. A note on pm-compact bipartite graphs. Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 409-413. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1706/
[1] C.A. Barefoot, R.C. Entringer and L.A. Sz´ekely, Extremal values for ratios of dis- tances in trees, Discrete Appl. Math. 80 (1997) 37-56. doi:10.1016/S0166-218X(97)00068-1[Crossref]
[2] A.A. Dobrynin, R. Entringer and I. Gutman, Wiener index of trees: theory and applications, Acta Appl. Math 66 (2001) 211-249. doi:10.1023/A:1010767517079[Crossref] | Zbl 0982.05044
[3] L. Johns and T.C. Lee, S-distance in trees, in: Computing in the 90’s (Kalamazoo, MI, 1989), Lecture Notes in Comput. Sci., 507, N.A. Sherwani, E. de Doncker and J.A. Kapenga (Ed(s)), (Springer, Berlin, 1991) 29-33. doi:10.1007/BFb0038469[Crossref]
[4] T. Lengyel, Some graph problems and the realizability of metrics by graphs, Congr. Numer. 78 (1990) 245-254 | Zbl 0862.05038