scholarly journals Hadwiger's Conjecture for 3-Arc Graphs

10.37236/5134 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
David R Wood ◽  
Guangjun Xu ◽  
Sanming Zhou
Keyword(s):  
Hadwiger's Conjecture ◽  
Hadwiger’S Conjecture

The 3-arc graph of a digraph $D$ is defined to have vertices the arcs of $D$ such that two arcs $uv, xy$ are adjacent if and only if $uv$ and $xy$ are distinct arcs of $D$ with $v\ne x$, $y\ne u$ and $u,x$ adjacent. We prove Hadwiger's conjecture for 3-arc graphs.

scholarly journals Hadwiger's Conjecture for ℓ-Link Graphs

2016 ◽  
Vol 84 (4) ◽  
pp. 460-476
Author(s):  
Bin Jia ◽  
David R. Wood
Keyword(s):  
Hadwiger's Conjecture ◽  
Hadwiger’S Conjecture

scholarly journals Improper colouring of graphs with no odd clique minor

2019 ◽  
Vol 28 (5) ◽  
pp. 740-754
Author(s):  
Dong Yeap Kang ◽  
Sang-Il Oum
Keyword(s):  
Maximum Degree ◽  
Hadwiger's Conjecture ◽  
Vertex Set ◽  
Bounded Size ◽  
Hadwiger’S Conjecture

AbstractAs a strengthening of Hadwiger’s conjecture, Gerards and Seymour conjectured that every graph with no oddKtminor is (t− 1)-colourable. We prove two weaker variants of this conjecture. Firstly, we show that for eacht⩾ 2, every graph with no oddKtminor has a partition of its vertex set into 6t− 9 setsV1, …,V6t−9such that eachViinduces a subgraph of bounded maximum degree. Secondly, we prove that for eacht⩾ 2, every graph with no odd Kt minor has a partition of its vertex set into 10t−13 setsV1,…,V10t−13such that eachViinduces a subgraph with components of bounded size. The second theorem improves a result of Kawarabayashi (2008), which states that the vertex set can be partitioned into 496tsuch sets.

scholarly journals Hadwiger's Conjecture for Graphs with Forbidden Holes

2017 ◽  
Vol 31 (3) ◽  
pp. 1572-1580 ◽  
Author(s):  
Zi-Xia Song ◽  
Brian Thomas
Keyword(s):  
Hadwiger's Conjecture ◽  
Hadwiger’S Conjecture

scholarly journals A case of hadwiger's conjecture

1973 ◽  
Vol 4 (3) ◽  
pp. 197-199
Author(s):  
Michael O. Albertson
Keyword(s):  
Hadwiger's Conjecture ◽  
Hadwiger’S Conjecture

scholarly journals Hadwiger's Conjecture for the Complements of Kneser Graphs

2015 ◽  
Vol 84 (1) ◽  
pp. 5-16 ◽  
Author(s):  
Guangjun Xu ◽  
Sanming Zhou
Keyword(s):  
Hadwiger's Conjecture ◽  
Kneser Graphs ◽  
Hadwiger’S Conjecture

Hadwiger's conjecture for quasi-line graphs

2008 ◽  
Vol 59 (1) ◽  
pp. 17-33 ◽  
Author(s):  
Maria Chudnovsky ◽  
Alexandra Ovetsky Fradkin
Keyword(s):  
Line Graphs ◽  
Hadwiger's Conjecture ◽  
Hadwiger’S Conjecture
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