Induced 2-degenerate Subgraphs of Triangle-free Planar Graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10385410" target="_blank" >RIV/00216208:11320/18:10385410 - isvavai.cz</a>

Result on the web

<a href="https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p62" target="_blank" >https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p62</a>

DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Induced 2-degenerate Subgraphs of Triangle-free Planar Graphs

Original language description

A graph is k degenerate if every subgraph has minimum degree at most k. We provide lower bounds on the size of a maximum induced 2-degenerate subgraph in a triangle-free planar graph. We denote the size of a maximum induced 2-degenerate subgraph of a graph G by alpha(2) (G). We prove that if G is a connected triangle-free planar graph with n vertices and rn edges, then alpha(2) (G) &gt;= 6n-m-1/5. By Euler&apos;s Formula, this implies alpha(2)(G) &gt;= 4/5n. We also prove that if G is a triangle-free planar graph on n vertices with at most n 3 vertices of degree at most three, then alpha(2) (G) &gt;= 7/8n - 18n(3.)

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GA17-04611S" target="_blank" >GA17-04611S: Ramsey-like aspects of graph coloring</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Electronic Journal of Combinatorics

ISSN

1077-8926

e-ISSN

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Volume of the periodical

25

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

18

Pages from-to

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UT code for WoS article

000432157200003

EID of the result in the Scopus database

2-s2.0-85044750950