Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Minimally colored trees.

I Rinsma1, M Hendy, D Penny

  • 1Department of Mathematics and Statistics, Waikato University, Hamilton, New Zealand.

Mathematical Biosciences
|March 1, 1990
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

IsProchlorothrix hollandica the best choice as a prokaryotic model for higher plant Chla/b photosynthesis?

Photosynthesis research·2013
Same author

Progress with methods for constructing evolutionary trees.

Trends in ecology & evolution·2011
Same author

Recovering evolutionary trees under a more realistic model of sequence evolution.

Molecular biology and evolution·2009
Same author

Genomics and the irreducible nature of eukaryote cells.

Science (New York, N.Y.)·2006
Same author

The MinMax Squeeze: guaranteeing a minimal tree for population data.

Molecular biology and evolution·2004
Same author

Outgroup misplacement and phylogenetic inaccuracy under a molecular clock--a simulation study.

Systematic biology·2003
Same journal

The hydra and hormetic effects in a single discrete-time overcompensation model.

Mathematical biosciences·2026
Same journal

Seasonal impacts on brucellosis transmission mediated by live sheep supply-demand dynamics.

Mathematical biosciences·2026
Same journal

Optimal controls and cost-effectiveness analysis on the transmission dynamics of early blight disease in tomatoes.

Mathematical biosciences·2026
Same journal

Temperature-dependent dynamics and allee effect thresholds mediate fourfold cusp stability in biological control of invasive vectors.

Mathematical biosciences·2026
Same journal

Dynamics of a stochastic tumor-immune interaction system with an Ornstein-Uhlenbeck process.

Mathematical biosciences·2026
Same journal

Post-peak dynamics and epidemic overshoot in SIR-type frameworks.

Mathematical biosciences·2026
See all related articles

This study introduces a method using generating functions to count minimal colorings and calculate average edge weights in weighted colored trees. These findings offer insights into evolutionary tree structures with efficient O(n) operations.

Area of Science:

  • Graph theory
  • Combinatorics
  • Computational biology

Background:

  • Weighted colored trees involve assigning nonnegative weights to edges based on incident vertex colors.
  • Minimal colorings aim to minimize the total tree weight using a finite set of colors.
  • Existing O(n) algorithms efficiently find minimal colorings.

Purpose of the Study:

  • To determine the number of minimal colorings for weighted colored trees.
  • To calculate the average weight of each edge across all minimal colorings.
  • To apply these combinatorial methods to the analysis of evolutionary trees.

Main Methods:

  • Utilizing generating functions to enumerate minimal colorings.
  • Applying O(n) computational operations for efficiency.

Related Experiment Videos

  • Analyzing the properties of weighted colored trees.

    • Main Results:

    • A method to count the exact number of minimal colorings.
    • A technique to compute the average edge weight over minimal colorings.
    • Demonstrated O(n) efficiency for both counting and averaging.

    Conclusions:

    • Generating functions provide an effective tool for analyzing minimal colorings in weighted colored trees.
    • The developed methods are computationally efficient, suitable for large datasets.
    • The approach has direct applications in understanding evolutionary relationships represented by trees.