A graph $G$ is stratified if its vertex set is partitioned into classes, called strata. If there are $k$ strata, then $G$ is $k$-stratified. These graphs were introduced to study problems in VLSI design. The strata in a stratified graph are also referred to as color classes. For a color $X$ in a stratified graph $G$, the $X$-eccentricity $e_X(v)$ of a vertex $v$ of $G$ is the distance between $v$ and an $X$-colored vertex furthest from $v$. The minimum $X$-eccentricity among the vertices of $G$ is the $X$-radius $\mathop {\mathrm rad}\nolimits _XG$ of $G$ and the maximum $X$-eccentricity is the $X$-diameter $\mathop {\mathrm diam}\nolimits _XG$. It is shown that for every three positive integers $a, b$ and $k$ with $a \le b$, there exist a $k$-stratified graph $G$ with $\mathop {\mathrm rad}\nolimits _XG=a$ and $\mathop {\mathrm diam}\nolimits _XG=b$. The number $s_X$ denotes the minimum $X$-eccetricity among the $X$-colored vertices of $G$. It is shown that for every integer $t$ with $\mathop {\mathrm rad}\nolimits _XG \le t \le \mathop {\mathrm diam}\nolimits _XG$, there exist at least one vertex $v$ with $e_X(v)=t$; while if $\mathop {\mathrm rad}\nolimits _XG \le t \le s_X$, then there are at least two such vertices. The $X$-center $C_X(G)$ is the subgraph induced by those vertices $v$ with $e_X(v)=\mathop {\mathrm rad}\nolimits _XG$ and the $X$-periphery $P_X(G)$ is the subgraph induced by those vertices $v$ with $e_X(G)=\mathop {\mathrm diam}\nolimits _XG$. It is shown that for $k$-stratified graphs $H_1, H_2, \dots , H_k$ with colors $X_1, X_2, \dots , X_k$ and a positive integer $n$, there exists a $k$-stratified graph $G$ such that $C_{X_i}(G) \cong H_i \ (1 \le i \le k)$ and $d(C_{X_i}(G), C_{X_j}(G)) \ge n \text{for} i \ne j$. Those $k$-stratified graphs that are peripheries of $k$-stratified graphs are characterized. Other distance-related topics in stratified graphs are also discussed.
The paper explores the close connection between social work and feminist movement and theory. He tradition and history of social work are incomplete without social workers - women activists. he aim of the paper is to examine the historical context of the professionalization of social work in close connection with the irst wave of feminism, and to interrogate positions which refuse feminist approaches in social work as marginal, ideological - not objective, or curious and even dangerous, improper. Women’s movement is one of the sources of development and professionalization of social work. Political and social activism of many outstanding women - “Mothers“ of social work - was an integral part of their professional career. his aspect of their lives is, however, all too often “forgotten“ in textbooks. he importance of pride, roots and the tradition is a fundamental aspect for every social work graduate and practitioner, especially as the status of social work in society has been falling., Monika Bosá., Poznámky, Obsahuje bibliografii, and Abstrakt a klíčová slova anglicky
This essay is a response to the discussion paper by Daniela Tinková on Enlightenment and vernacularization. The author welcomes the approach that sees Enlightenment as a debate, since to see it as a battle is to confuse logical truth with fiction. It should be said, however, that Tinková’s model attributes an active role only to the elites, and overstates the idea of the disappearance of the state. In the 18th century we may not have had a national state, but we did have a state. A common fallacy among Czechs regarding the timing and mechanism of the emergence of the National Revival is to ignore that state and consequently espouse the unrealistic thesis that the national agitation arose among a free people in the repressive period preceding March 1848. They also fail to appreciate the importance of the constitutional monarchy post-1861, when for the first time Czechs were able to engage in free political debate. As a result it was not until the late 19th century that a belated Czech Enlightenment took hold, inspired largely by France and Scotland. Home-grown Enlightenment traditions had by then been forgotten.