Excluding a Ladder
نویسندگان
چکیده
A ladder is a 2 × k grid graph. When does graph class $${\cal C}$$ exclude some as minor? We show that this the case if and only all graphs G in admit proper vertex coloring with bounded number of colors such for every 2-connected subgraph H G, there color appears exactly once H. This type relaxation notion centered coloring, where connected must be The minimum treedepth it known classes are those fixed path subgraph, or equivalently, minor. In sense, structure excluding minor resembles without long paths. Another similarity follows: It an easy observation two vertex-disjoint paths length has k+1. 3-connected which contains union sufficiently many copies 2×k 2×(k+1) Our structural results have applications to poset dimension. posets whose cover new step towards goal understanding unavoidable minors large
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2021
ISSN: ['0209-9683', '1439-6912']
DOI: https://doi.org/10.1007/s00493-021-4592-8