Colouring Graphs with No Induced Six-Vertex Path or Diamond
نویسندگان
چکیده
The diamond is the graph obtained by removing an edge from complete on 4 vertices. A (\(P_6\), diamond)-free if it contains no induced subgraph isomorphic to a six-vertex path or diamond. In this paper we show that chromatic number of G larger than maximum 6 and clique G. We do reducing problem imperfect graphs via Strong Perfect Graph Theorem, dividing into several cases, giving proper colouring for each case. also there exactly one 6-vertex-critical diamond, \(K_6\))-free graph. Together with Lovász theta function, gives polynomial time algorithm compute graphs.
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ژورنال
عنوان ژورنال: Lecture Notes in Computer Science
سال: 2021
ISSN: ['1611-3349', '0302-9743']
DOI: https://doi.org/10.1007/978-3-030-89543-3_27