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The split graph on vertices is denoted by . A non-increasing sequence of nonnegative integers is said to be potentially -graphic if there exists a realization of containing as a subgraph. In this paper, we obtain a Havel-Hakimi type procedure and a simple sufficient condition for to be potentially -graphic. They are extensions of two theorems due to A. R. Rao (The clique number of a graph with given degree sequence, Graph Theory, Proc. Symp., Calcutta 1976, ISI Lect. Notes Series...
The 'two paths problem' is stated as follows. Given an undirected graph G = (V,E) and vertices s₁,t₁;s₂,t₂, the problem is to determine whether or not G admits two vertex-disjoint paths P₁ and P₂ connecting s₁ with t₁ and s₂ with t₂ respectively. In this paper we give a linear (O(|V|+ |E|)) algorithm to solve the above problem on a permutation graph.
In this work, we get a combinatorial characterization for maximal generalized outerplanar graphs (mgo graphs). This result yields a recursive algorithm testing whether a graph is a mgo graph or not.
ACM Computing Classification System (1998): G.2.2.We propose an algorithm that computes the length of a longest
path in a cactus graph. Our algorithm can easily be modified to output a
longest path as well or to solve the problem on cacti with edge or vertex
weights. The algorithm works on rooted cacti and assigns to each vertex
a two-number label, the first number being the desired parameter of the
subcactus rooted at that vertex. The algorithm applies the divide-and-conquer approach and computes...
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