$\chi$-bounds, operations and chords
نویسندگان
چکیده
A long unichord in a graph is an edge that is the unique chord of some cycle of length at least 5. A graph is long-unichord-free if it does not contain any long-unichord. We prove a structure theorem for long-unichord-free graph. We give an O(nm)-time algorithm to recognize them. We show that any long-unichord-free graph G can be colored with at most O(ω) colors, where ω is the maximum number of pairwise adjacent vertices in G.
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