Equimatchable Graphs on Surfaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F16%3A00089064" target="_blank" >RIV/00216224:14330/16:00089064 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1002/jgt.21859" target="_blank" >http://dx.doi.org/10.1002/jgt.21859</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.21859" target="_blank" >10.1002/jgt.21859</a>

Result language
angličtina
Original language name
Equimatchable Graphs on Surfaces
Original language description
A graph G is equimatchable if each matching in G is a subset of a maximum-size matching and it is factor critical if G - v has a perfect matching for each vertex v of G. It is known that any 2-connected equimatchable graph is either bipartite or factor critical. We prove that for 2-connected factor-critical equimatchable graph G the graph G(V(M) U {v}) is either K_{2n} or K_{n,n} for some n for any vertex v of G and any minimal matching M such that {v} is a component of GV(M). We use this result to improve the upper bounds on the maximum number of vertices of 2-connected equimatchable factor-critical graphs embeddable in the orientable surface of genus g to 4sqrt{g} + 17 if g <= 2 and to 12sqrt{g} + 5 if g >= 3. Moreover, for any nonnegative integer g we construct a 2-connected equimatchable factor-critical graph with genus g and more than 4sqrt{2g} vertices, which establishes that the maximum size of such graphs is Theta(sqrt{g}).
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
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Project
<a href="/en/project/EE2.3.30.0009" target="_blank" >EE2.3.30.0009: Employment of Newly Graduated Doctors of Science for Scientific Excellence</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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