Borodin–Kostochka’s conjecture on (P5,C4)-free graphs
Brooks’ theorem states that for a graph G , if Δ ( G ) ≥ 3 , then χ ( G ) ≤ max { Δ ( G ) , ω ( G ) } . Borodin and Kostochka conjectured a result strengthening Brooks’ theorem, stated as, if Δ ( G ) ≥ 9 , then χ ( G ) ≤ max { Δ ( G ) - 1 , ω ( G ) } . This conjecture is still open for general graph...
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Published in | Journal of applied mathematics & computing Vol. 65; no. 1-2; pp. 877 - 884 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.02.2021
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | Brooks’ theorem states that for a graph
G
, if
Δ
(
G
)
≥
3
, then
χ
(
G
)
≤
max
{
Δ
(
G
)
,
ω
(
G
)
}
. Borodin and Kostochka conjectured a result strengthening Brooks’ theorem, stated as, if
Δ
(
G
)
≥
9
, then
χ
(
G
)
≤
max
{
Δ
(
G
)
-
1
,
ω
(
G
)
}
. This conjecture is still open for general graphs. In this paper, we show that the conjecture is true for graphs having no induced path on five vertices and no induced cycle on four vertices. |
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ISSN: | 1598-5865 1865-2085 |
DOI: | 10.1007/s12190-020-01419-3 |