Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647726 | Discrete Mathematics | 2013 | 7 Pages |
Abstract
We prove that if GG is a vertex-critical graph with χ(G)≥Δ(G)+1−p≥4χ(G)≥Δ(G)+1−p≥4 for some p∈Np∈N and ω(H(G))≤χ(G)+1p+1−2, then G=Kχ(G)G=Kχ(G) or G=O5G=O5. Here H(G)H(G) is the subgraph of GG induced on the vertices of degree at least χ(G)χ(G). This simplifies the proofs and improves the results in the paper of Kostochka, Rabern and Stiebitz (2012) [8].
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Landon Rabern,