We study efficient exact algorithms for several problems including Vertex Bipartization, Feedback Vertex Set, 3-Hitting Set, Max Cut in graphs with maximum degree at most 4. Our main results include: 1. an O(1.9526) 1 algorithm for Vertex Bipartization problem in undirected graphs; 2. an O(1.8384) algorithm for Vertex Bipartization problem in undirected graphs of maximum degree 3; 3. an O(1.945...

Interconnection Networks are a boon to human made large computing systems which often designed based on the need. In this paper, we address question of obtaining an interconnection network suit specific need is cumbersome procedure. The methods for constructing infinitely networks from any simple, undirected graph \(G\) illustrated and their properties discussed. Further, study behaviour certai...

Let D be a directed graph of order n 4 and minimum degree at least (3n 3)/2. Let n = nI + n2 where nl 2 and n2 2. Then D contains two vertex-disjoint directed cycles of nI and n2 respectively. The result is sharp if n ~ 6: we give counterexamples if the condition on the minimum degree is relaxed. 1 Introduction We discuss only finite simple graphs and strict and use standard terminology and not...

We investigate minimum vertex degree conditions for 3-uniform hypergraphs which ensure the existence of loose Hamilton cycles. A loose Hamilton cycle is a spanning cycle in which consecutive edges intersect in a single vertex. We prove that every 3-uniform n-vertex (n even) hypergraph H with minimum vertex degree δ1(H) ≥ ( 7 16 + o(1) ) ( n 2 ) contains a loose Hamilton cycle. This bound is asy...