# Gallai's innequality for critical graphs of reducible hereditary properties

• Volume: 21, Issue: 2, page 167-177
• ISSN: 2083-5892

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## Abstract

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In this paper Gallai’s inequality on the number of edges in critical graphs is generalized for reducible additive induced-hereditary properties of graphs in the following way. Let $₁,₂,...,ₖ$ (k ≥ 2) be additive induced-hereditary properties, $=₁\circ ₂\circ ...\circ ₖ$ and $\delta ={\sum }_{i=1}^{k}\delta {\left(}_{i}\right)$. Suppose that G is an -critical graph with n vertices and m edges. Then 2m ≥ δn + (δ-2)/(δ²+2δ-2)*n + (2δ)/(δ²+2δ-2) unless = ² or $G={K}_{\delta +1}$. The generalization of Gallai’s inequality for -choice critical graphs is also presented.

## How to cite

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Peter Mihók, and Riste Skrekovski. "Gallai's innequality for critical graphs of reducible hereditary properties." Discussiones Mathematicae Graph Theory 21.2 (2001): 167-177. <http://eudml.org/doc/270179>.

@article{PeterMihók2001,
abstract = {In this paper Gallai’s inequality on the number of edges in critical graphs is generalized for reducible additive induced-hereditary properties of graphs in the following way. Let $₁,₂,...,ₖ$ (k ≥ 2) be additive induced-hereditary properties, $= ₁ ∘ ₂ ∘ ... ∘ₖ$ and $δ = ∑_\{i=1\}^k δ(_i)$. Suppose that G is an -critical graph with n vertices and m edges. Then 2m ≥ δn + (δ-2)/(δ²+2δ-2)*n + (2δ)/(δ²+2δ-2) unless = ² or $G = K_\{δ+1\}$. The generalization of Gallai’s inequality for -choice critical graphs is also presented.},
author = {Peter Mihók, Riste Skrekovski},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {additive induced-hereditary property of graphs; reducible property of graphs; critical graph; Gallai's Theorem; Gallai's inequality; critical graphs},
language = {eng},
number = {2},
pages = {167-177},
title = {Gallai's innequality for critical graphs of reducible hereditary properties},
url = {http://eudml.org/doc/270179},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Peter Mihók
AU - Riste Skrekovski
TI - Gallai's innequality for critical graphs of reducible hereditary properties
JO - Discussiones Mathematicae Graph Theory
PY - 2001
VL - 21
IS - 2
SP - 167
EP - 177
AB - In this paper Gallai’s inequality on the number of edges in critical graphs is generalized for reducible additive induced-hereditary properties of graphs in the following way. Let $₁,₂,...,ₖ$ (k ≥ 2) be additive induced-hereditary properties, $= ₁ ∘ ₂ ∘ ... ∘ₖ$ and $δ = ∑_{i=1}^k δ(_i)$. Suppose that G is an -critical graph with n vertices and m edges. Then 2m ≥ δn + (δ-2)/(δ²+2δ-2)*n + (2δ)/(δ²+2δ-2) unless = ² or $G = K_{δ+1}$. The generalization of Gallai’s inequality for -choice critical graphs is also presented.
LA - eng
KW - additive induced-hereditary property of graphs; reducible property of graphs; critical graph; Gallai's Theorem; Gallai's inequality; critical graphs
UR - http://eudml.org/doc/270179
ER -

## References

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