No abstract

The p-spectral radius of a uniform hypergraph G of order n is defined for every real number p ≥ 1 as λ (p) (G) = maxIt generalizes several hypergraph parameters, including the Lagrangian, the spectral radius, and the number of edges. The paper presents solutions to several extremal problems about the p-spectral radius of k-partite and k-chromatic hypergraphs of order n. Two of the main results are: (I) Let k ≥ r ≥ 2, and let G be a k-partite r-graph of order n. For every p > 1,is the complete k-partite r-graph of order n, with parts of size ⌊n/k⌋ or ⌈n/k⌉.(II) Let k ≥ 2, and let G be a k-chromatic 3-graph of order n. For every p ≥ 1,is a complete k-chromatic 3-graph of order n, with classes of size ⌊n/k⌋ or ⌈n/k⌉.The latter statement generalizes a result of Mubayi and Talbot.

We study a scheduling problem with deteriorating jobs, i.e., jobs whose processing times are an increasing function of their start times.We consider the case of a single machine and linear job-independent deterioration. The problem is to determine an optimal combination of the due date and schedule so as to minimize the sum of due-date, earliness and tardiness penalties. We give an O(n logn) time algorithm to solve this problem.

We study the paired-domination problem on interval graphs and circular-arc graphs. Given an interval model with endpoints sorted, we give an O(m + n) time algorithm to solve the paired-domination problem on interval graphs. The result is extended to solve the paired-domination problem on circular-arc graphs in O(m(m + n)) time.