We present a novel, yet simple, technique for the speciication of context in structured documents that we call caterpillar expressions. Although we are primarily applying this technique in the speciication of context-dependent style sheets for HTML, SGML and XML documents, it can also be used for query speciica-tion for structured documents, as we shall demonstrate, and for the speciication of ...

We present a novel, yet simple, technique for the speciication of context in struc-tured documents that we call caterpillar expressions. Although we are primarily applying this technique in the speciication of context-dependent style sheets for HTML, SGML and XML documents, it can also be used for query speciication for structured documents, as we shall demonstrate, and for the speciication of ...

A caterpillar is a tree which metamorphoses into a path when its cocoon of endpoInt\ is removed. The number of nonisomorphic caterpillars with n + 4 points is 2n + 2 [n/21 . This neat formula is proved in two ways: first, as a special caoe of an application of Pblya’s enumerration theorem which counts graphs with integer-weightell points; secondly, 3y an appropriate labeling of the lines of the...

We study caterpillar tree automata [3] that are restricted to enter any subtree at most one time (or k times). We show that, somewhat surprisingly, the deterministic one-visit automata can already, for instance, evaluate trees where the nodes represent some non-associative operations. We show that there exist regular tree languages that cannot be accepted by a one-visit automaton, thus proving ...

A connected graph G is caterpillar-pure if each spanning tree of G is a caterpillar. The caterpillar-pure graphs are fully characterized. Loosely speaking they are strings or necklaces of so-called pearls, except for a number of small exceptional cases. An upper bound for the number of edges in terms of the order is given for caterpillar-pure graphs, and those which attain the upper bound are c...

A graph G is called a pairwise compatibility graph (PCG) if there exists an edge-weighted tree T and two non-negative real numbers dmin and dmax such that each leaf lu of T corresponds to a vertex u ∈ V and there is an edge (u, v) ∈ E if and only if dmin ≤ dT,w(lu, lv) ≤ dmax where dT,w(lu, lv) is the sum of the weights of the edges on the unique path from lu to lv in T . In this paper, we conc...

A tree is called a caterpillar if all its leaves are adjacent to the same its path, and the path is called a spine of the caterpillar. Broersma and Tuinstra proved that if a connected graph G satisfies σ2(G) ≥ |G| − k + 1 for an integer k ≥ 2, then G has a spanning tree having at most k leaves. In this paper we improve this result as follows. If a connected graph G satisfies σ2(G) ≥ |G|−k+1 and...

In this paper we have further elaborated MPLS multicasting under the specific graph (graceful) labeling with the use of specific multicast tree topology called caterpillar which is next higher topological structure other than the path; that is a central concept in the IP unicast routing. The use of caterpillar as the multicast tree has been analyzed and compared with the other tree topologies u...

Tree-width and its linear variant path-width play a central role for the graph minor relation. In particular, Robertson Seymour (1983) proved that every tree~$T$, class of graphs do not contain $T$ as has bounded path-width. For pivot-minor relation, rank-width take over from tree-width As such, it is natural to examine if rank-width. We first prove this statement false whenever tree caterpilla...

A caterpillar graph is a tree in which the removal of all pendant vertices results in a chordless path. In this work, we determine the number of maximal independent sets (mis) in caterpillar graphs. For a general graph, this problem is #P—complete. We provide a polynomial time algorithm to generate the whole family of mis in a caterpillar graph. We also characterize the independent graph (inter...