{"paper":{"title":"Graphs of Edge-Intersecting Non-Splitting Paths in a Tree: Towards Hole Representations-Part I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Arman Boyac{\\i}, Mordechai Shalom, Shmuel Zaks, T{\\i}naz Ekim","submitted_at":"2013-09-11T17:30:59Z","abstract_excerpt":"Given a tree and a set ${\\cal P}$ of non-trivial simple paths on it, $VPT({\\cal P})$ is the VPT graph (i.e. the vertex intersection graph) of the paths ${\\cal P}$ of the tree $T$, and $EPT({\\cal P})$ is the EPT graph (i.e. the edge intersection graph) of ${\\cal P}$. These graphs have been extensively studied in the literature. Given two (edge) intersecting paths in a graph, their \\emph{split vertices} is the set of vertices having degree at least $3$ in their union. A pair of (edge) intersecting paths is termed \\emph{non-splitting} if they do not have split vertices (namely if their union is a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2898","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}