For a nontrivial connected graph $F$, the $F$-degree of a vertex $v$ in a graph $G$ is the number of copies of $F$ in $G$ containing $v$. A graph $G$ is $F$-continuous (or $F$-degree continuous) if the $F$-degrees of every two adjacent vertices of $G$ differ by at most 1. All $P_3$-continuous graphs are determined. It is observed that if $G$ is a nontrivial connected graph that is $F$-continuous for all nontrivial connected graphs $F$, then either $G$ is regular or $G$ is a path. In the case of a 2-connected graph $F$, however, there always exists a regular graph that is not $F$-continuous. It is also shown that for every graph $H$ and every 2-connected graph $F$, there exists an $F$-continuous graph $G$ containing $H$ as an induced subgraph.
The paper deals with important elements of Tibetan identity. The first part is devoted to the general issues of Tibetan identity, i.e. the shared religion (Tibetan Buddhism), language, the myth of the origin of Tibetans, ethnographical features (food, dress), the territory inhabited by Tibetans. It discusses issues related to the existence/non-existence of pan-Tibetan identity and the strong regional identities. The secondpart concentrates on the issue of regional identity in Amdo (north-eastern part of Tibetan Plateau), mainly in the area around the Labrang (bia brang) monastery. The identity of Amdo Tibetans is represented by distinctive myths of origin, special dialect and also in the realm of folk religion. Especially mountain cults play an important role in the constitution of micro-identity of individual tribes. The local identity near the Labrang monastery is being established also through the net of relations between individual reincarnations (Tib. tulku, sprul sku) of Labrang and the sedentary and nomad Tibetan communities. This traditional relationships (in Tibetan called lharde, lha sde, „divine community“, and mirde, mi sde, „human community“) are also now in function. The other lev el of religious identity centered around the Labrang monastery is the web of relations between the main monastery (in Tibetan magön, ma dgon, „mother monastery“), i.e. Labrang, and over 90 smaller monasteries in the wholeAmdo area which are subordinated branches (in Tibetan, gönlag, dgon lag , „monastery limbs“) of Labrang. The interethnic aspect of the constitution of Tibetan identity plays also an important role in the ethnically diverse region ofAmdo with strong presence of Muslim Chinese (Hui) and Han-Chinese population.