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- W2891037588 abstract "This thesis deals with graph coloring, list-coloring, maximum weightstable set (shortened as MWSS) and structural graph theory.First, we provide polynomial-time algorithms for the 4-coloring problem insubclasses of $P_6$-free graphs. These algorithms rely on a preciseunderstanding of the structure of these classes of graphs for which we give afull description.Secondly, we study the list-coloring conjecture and prove that for anyclaw-free perfect graph with clique number bounded by 4, the chromatic numberand the choice number are equal. This result is obtained by using adecomposition theorem for claw-free perfect graphs, a structural description ofthe basic graphs of this decomposition and by using Galvin's famous theorem.Next by using the structural description given in the first chapter andstrengthening other aspects of this structure, we provide polynomial-timealgorithms for the MWSS problem in subclasses of $P_6$-free and $P_7$-freegraphs.In the last chapter of the manuscript, we disprove a conjecture of De Simoneand Korner made in 1999 related to normal graphs. Our proof is probabilisticand is obtained by the use of random graphs." @default.
- W2891037588 created "2018-09-27" @default.
- W2891037588 creator A5014495214 @default.
- W2891037588 date "2017-11-23" @default.
- W2891037588 modified "2023-09-25" @default.
- W2891037588 title "Coloring, stable set and structure of graphs" @default.
- W2891037588 hasPublicationYear "2017" @default.
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