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A note on uniquely 10‐colorable graphs
Author(s) -
Kriesell Matthias
Publication year - 2021
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22679
Subject(s) - mathematics , combinatorics , brooks' theorem , chromatic scale , graph coloring , clique number , fractional coloring , discrete mathematics , list coloring , edge coloring , graph , split graph , clique , 1 planar graph , chordal graph , graph power , line graph
Hadwiger conjectured that every graph of chromatic number k admits a clique minor of order k . Here we prove for k ≤ 10 , that every graph of chromatic number k with a unique k ‐coloring (up to the color names) admits a clique minor of order k . The proof does not rely on the Four Color Theorem.