کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9515947 1343748 2005 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Path decompositions and Gallai's conjecture
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Path decompositions and Gallai's conjecture
چکیده انگلیسی
Let G be a connected simple graph on n vertices. Gallai's conjecture asserts that the edges of G can be decomposed into ⌈n2⌉ paths. Let H be the subgraph induced by the vertices of even degree in G. Lovász showed that the conjecture is true if H contains at most one vertex. Extending Lovász's result, Pyber proved that the conjecture is true if H is a forest. A forest can be regarded as a graph in which each block is an isolated vertex or a single edge (and so each block has maximum degree at most 1). In this paper, we show that the conjecture is true if H can be obtained from the emptyset by a series of so-defined α-operations. As a corollary, the conjecture is true if each block of H is a triangle-free graph of maximum degree at most 3.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series B - Volume 93, Issue 2, March 2005, Pages 117-125
نویسندگان
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