Two trees in maximal planar bipartite graphs

Maximal independent sets in bipartite gr

Maximal independent sets in bipartite graphs

✍ Jiuqiang Liu 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 458 KB 👁 1 views

## Abstract A maximal independent set of a graph __G__ is an independent set that is not contained properly in any other independent set of __G.__ In this paper, we determine the maximum number of maximal independent sets among all bipartite graphs of order __n__ and the extremal graphs as well as

Maximizing spanning trees in almost comp

Maximizing spanning trees in almost complete graphs

✍ Gilbert, Bryan; Myrvold, Wendy 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 94 KB 👁 2 views

We examine the family of graphs whose complements are a union of paths and cycles and develop a very simple algebraic technique for comparing the number of spanning trees. With our algebra, we can obtain a simple proof of a result of Kel'mans that evening out path lengths increases the number of spa

Maximizing spanning trees in almost comp

Maximizing spanning trees in almost complete graphs

✍ Gilbert, Bryan; Myrvold, Wendy 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 94 KB 👁 2 views

We examine the family of graphs whose complements are a union of paths and cycles and develop a very simple algebraic technique for comparing the number of spanning trees. With our algebra, we can obtain a simple proof of a result of Kel'mans that evening-out path lengths increases the number of spa

Alternating hamiltonian cycles in two co

Alternating hamiltonian cycles in two colored complete bipartite graphs

✍ A. G. Chetwynd; A. J. W. Hilton 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 269 KB 👁 2 views

## Abstract We give necessary and sufficient conditions for the existence of an alternating Hamiltonian cycle in a complete bipartite graph whose edge set is colored with two colors.

Special monochromatic trees in two-color

Special monochromatic trees in two-colored complete graphs

✍ Chen, Guantao; Schelp, Richard H.; ?olt�s, ?ubom�r 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 106 KB 👁 2 views

For a positive integer k, a set of k + 1 vertices in a graph is a k-cluster if the difference between degrees of any two of its vertices is at most k -1. Given any tree T with at least k 3 edges, we show that for each graph G of sufficiently large order, either G or its complement contains a copy of

Two-Connected Augmentation Problems in P

Two-Connected Augmentation Problems in Planar Graphs

✍ J.Scott Provan; Roger C Burk 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 167 KB

Given a weighted undirected graph G and a subgraph S of G, we consider the problem of adding a minimum-weight set of edges of G to S so that the resulting Ž . subgraph satisfies specified edge or vertex connectivity requirements between pairs of nodes of S. This has important applications in upgradi

Two trees in maximal planar bipartite graphs

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