Fundamentals of factor theory.- Factors and graphic parameters.- (g,f )-factor and factorization.- Component factors and connected factors.- Elementary graphs and decomposition.- Extendable graphs with special properties.- k-extendable graphs and n-factor-critical graphs.- Fractional factors.

/pdf/graph-factors-and-matching-extensions-1zrod7pa4i.pdf

Graph Factors and Matching Extensions

https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0012365X_v309_n18_p5618_Lin.pdf

Characterizations and recognition of circular-arc graphs and subclasses: A survey

The longest path problem is the one that finds a longest path in a given graph. While the graph classes in which the Hamiltonian path problem can be solved efficiently are widely investigated, few graph classes are known to be solved efficiently for the longest path problem. Among those, for trees, a simple linear time algorithm for the longest path problem is known. We first generalize the algorithm, and show that the longest path problem can be solved efficiently for some tree-like graph classes by this approach. We next propose two new graph classes that have natural interval representations, and show that the longest path problem can be solved efficiently on these classes.

/pdf/on-computing-longest-paths-in-small-graph-classes-1539ocoeoy.pdf

On computing longest paths in small graph classes

We study circular choosability, a notion recently introduced by Mohar and Zhu. First, we provide a negative answer to a question of Zhu about circular cliques. We next prove that cch(G)=O(ch(G)+ln|V(G)|) for every graph G. We investigate a generalization of circular choosability, the circular f-choosability, where f is a function of the degrees. We also consider the circular choice number of planar graphs. Mohar asked for the value of τ c suplcch(G) : G is planarr, and we prove that 6≤τ≤8, thereby providing a negative answer to another question of Mohar. We also study the circular choice number of planar and outerplanar graphs with prescribed girth, and graphs with bounded density. © 2009 Wiley Periodicals, Inc. J Graph Theory 61: 241–270, 2009

The research in this paper was carried out while the second and third authors were doctoral research students at the University of Oxford and the last author was a doctoral research student at MASCOTTE.

Circular choosability

? Users may download and print one copy of any publication from the public portal for the purpose of private study or research. ? You may not further distribute the material or use it for any profit-making activity or commercial gain ? You may freely distribute the URL identifying the publication in the public portal ? Take down policy If you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access to the work immediately and investigate your claim.

/pdf/connected-factors-in-graphs-a-survey-1eowe33frl.pdf

Connected Factors in Graphs --- a Survey

The interval number of a graph G is the least natural number t such that G is the intersection graph of sets, each of which is the union of at most t intervals, denoted by i(G). Griggs and West showed that $i(G)\le \lceil {1\over 2} (d+1)\rceil $. We describe the extremal graphs for that inequality when d is even. For three special perfect graph classes we give bounds on the interval number in terms of the independence number. Finally, we show that a graph needs to contain large complete bipartite induced subgraphs in order to have interval number larger than the random graph on the same number of vertices. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 241–253, 2004

/pdf/on-the-interval-number-of-special-graphs-3qqsmp4lq3.pdf

On the interval number of special graphs

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Pascal Ochem

Author Tools

Chat about Author

Papers

On the interval number of special graphs