“Whoa! It’s like Spotify but for academic articles.”

Instant Access to Thousands of Journals for just $40/month

Try 2 weeks free now

Representing edge intersection graphs of paths on degree 4 trees

Let P be a collection of nontrivial simple paths on a host tree T . The edge intersection graph of P , denoted by EPT ( P ) , has vertex set that corresponds to the members of P , and two vertices are joined by an edge if and only if the corresponding members of P share at least one common edge in T . An undirected graph G is called an edge intersection graph of paths in a tree if G = EPT ( P ) for some P and T . The EPT graphs are useful in network applications. Scheduling undirected calls in a tree network or assigning wavelengths to virtual connections in an optical tree network are equivalent to coloring its EPT graph. An undirected graph G is chordal if every cycle in G of length greater than 3 possesses a chord. Chordal graphs correspond to vertex intersection graphs of subtrees on a tree. An undirected graph G is weakly chordal if every cycle of length greater than 4 in G and in its complement G ‾ possesses a chord. It is known that the EPT graphs restricted to host trees of vertex degree 3 are precisely the chordal EPT graphs. We prove a new analogous result that weakly chordal EPT graphs are precisely the EPT graphs with host tree restricted to degree 4. Moreover, this provides an algorithm to reduce a given EPT representation of a weakly chordal EPT graph to an EPT representation on a degree 4 tree. Finally, we raise a number of intriguing open questions regarding related families of graphs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Discrete Mathematics Elsevier
Loading next page...

You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy unlimited access and
personalized recommendations from
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $40/month

Try 2 weeks free now

Explore the DeepDyve Library

How DeepDyve Works

Spend time researching, not time worrying you’re buying articles that might not be useful.

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from Springer, Elsevier, Nature, IEEE, Wiley-Blackwell and more.

All the latest content is available, no embargo periods.

See the journals in your area

Simple and Affordable Pricing

14-day free trial. Cancel anytime, with a 30-day money-back guarantee.

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Best Deal — 25% off

Annual Plan

  • All the features of the Professional Plan, but for 25% off!
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

billed annually