%0 Journal Article
%A Radovanović, Marko
%E Trotignon, Nicolas
%E Vušković, Kristina
%D 2019
%G English
%T The (theta, wheel)-free graphs Part IV: induced paths and cycles
%U http://bonn.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwdV1NSwMxEB3aehFEFJX6SQ4eFAzuppvtxpMiLXqweqgiXsrkCxVZpbt-_Xsn2RW8eA4E8oYw7yUzbwD2iVFTmkXNCx--GW0muSq84R4TdMTmMq9C7_DVRI0f8ulITTrAfnthcP719NH4A-vqmMRE8NOUad6FrhBxNMP1fdv70pRpPZtak8wTSbThDK8jC3GPP1livALLLb1jZ008VqHjyjU4pViwA2JaNR6xz0fnXg65nzvHolt0xW4ofOzy7oSRPiakLQtjgitGGp-Z71C1tg6349H0_IK3kws40oWpudYy9VIObeIFClIEWroCpTM22LHoNNd-SNQpzxNrrfHW60FmlJFOOAJH2MEGLGGocC_r2Aln-8AyFZJJajKNOvO6QJN4SuBojZUmxWIT-vHgs7fGpmIWwJtF8Lb-X9qGRaIAqinQ2IFePX93u9DTr2W5F8H-AbyzfZM
%X A hole in a graph is a chordless cycle of length at least 4. A theta is a
graph formed by three internally vertex-disjoint paths of length at least 2
between the same pair of distinct vertices. A wheel is a graph formed by a hole
and a node that has at least 3 neighbors in the hole. In this series of papers
we study the class of graphs that do not contain as an induced subgraph a theta
nor a wheel. In Part II of the series we prove a decomposition theorem for this
class, that uses clique cutsets and 2-joins. In this paper we use this
decomposition theorem to solve several problems related to finding induced
paths and cycles in our class.
%K Mathematics - Combinatorics