Dvořák’s five symphonic poems, composed between 1896 and 1897, attempt to bridge the antagonism existing between pure and programmatic music. Trying to overcome their typical differences, Dvořák reconciled the characteristic features of poetry and folklore with grand classical forms, demonstrating in this way his ability to utilise Liszt’s model and transform it by creating a new concept of programmatic music founded on the use of the Czech folkloric heritage. Four of the five poems are based on ballads by K. J. Erben, taken from the poetry book, The Bouquet (Kytice), where Dvořák found the sense of wonder, where simplicity meets with moral strength. Dvořák underlines the narration and the folk tone, applying the new processes which are based on the unity of poetic and musical setting. He, who initiated truly national music, models his orchestral ideas on the rhythms and intonations of the poetic text, creating a musical expression which conforms to the Czech character of the poem, opening in this way the path for Janáček. The folkloric character and his treatment of music setting, based on the will to translate as closely as possible the Czech soul, make these works an elaborate synthesis of Dvořák’s aspirations of appeasement between learned music and folklore.
A perfect independent set I of a graph G is defined to be an independent set with the property that any vertex not in I has at least two neighbors in I. For a nonnegative integer k, a subset I of the vertex set V (G) of a graph G is said to be k-independent, if I is independent and every independent subset I' of G with |I' | ≥ |I| − (k − 1) is a subset of I. A set I of vertices of G is a super k-independent set of G if I is k-independent in the graph G[I, V (G) − I], where G[I, V (G) − I] is the bipartite graph obtained from G by deleting all edges which are not incident with vertices of I. It is easy to see that a set I is 0-independent if and only if it is a maximum independent set and 1-independent if and only if it is a unique maximum independent set of G. In this paper we mainly investigate connections between perfect independent sets and k-independent as well as super k-independent sets for k = 0 and k = 1.