We examine the bandwidth problem in circular-arc graphs, chordal graphs with a bounded number of leaves in the clique tree, and k-polygon graphs (fixed k). We show that all of these graph classes admit efficient approximation algorithms which are based on exact or approximate bandwidth layouts of related interval graphs. Specifically, we obtain a bandwidth approximation algorithm for circular-a...

We study the problem of designing fault-tolerant routings with small routing tables for a kconnected network of n processors in the surviving route graph model. The surviving route graph R(G,ρ)/F for a graph G, a routing ρ and a set of faults F is a directed graph consisting of nonfaulty nodes of G with a directed edge from a node x to a node y iff there are no faults on the route from x to y. ...

A 1978 theorem of Kozen states that two graphs on n vertices are isomorphic if and only if there is a clique of size n in the weak modular product between the two graphs. Restricting to bipartite graphs and considering complete bipartite subgraphs (bicliques) therein, we study the combinatorics of the weak modular product. We identify cases where isomorphism is tractable using this approach, wh...

The strong truncated Hamburger moment problem (STHMP) of degree (?2k1,2k2) asks to find necessary and sufficient conditions for the existence a positive Borel measure, supported on R, such that ?i=?xid?(?2k1?i?2k2). first solution STHMP, covering also its matrix generalization, was established by Simonov [60], who used operator approach described all solutions in terms self-adjoint extensions c...

In this paper we prove that there exist 4—{k2; 1/2k(k—1); k(k—2)} SDS, regular Hadamard matrices of order 4k2, and SBIBD(4k2, 2k2 + k, k2 + k) for k = 47, 71, 151, 167, 199, 263, 359, 439, 599, 631, 727, 919, 5q1, 5q2N, 7q3, where ql, q2 and q3 are prime power such that ql ≡ 1(mod 4), q2 ≡ 5(mod 8) and q3 ≡ 3(mod 8), N = 2a3bt2, a, b = 0 or 1, t ≠ 0 is an arbitrary integer. We find new SBIBD(4k...

Strictly Chordality-k graphs (SCk) are graphs which are either cycle-free or every induced cycle is of length exactly k, k ≥ 3. Strictly chordality-3 and strictly chordality-4 graphs are well known chordal and chordal bipartite graphs, respectively. For k ≥ 5, the study has been recently initiated in [1] and various structural and algorithmic results are reported. In this paper, we show that ma...

Designing networks in which every processor has a given number of connections often leads to graphic degree sequence realization models. A nonincreasing sequence d = (d1, d2, . . . , dn) is graphic if there is a simple graphGwith degree sequence d. The spanning tree packing number of graphG, denoted by τ(G), is themaximumnumber of edge-disjoint spanning trees in G. The arboricity of graph G, de...