Gallai's Conjecture For Graphs of Girth at Least Four
نویسندگان
چکیده
In 1966, Gallai conjectured that for any simple, connected graph G having n vertices, there is a path-decomposition of G having at most dn2 e paths. In this paper, we show that for any simple graph G having girth g ≥ 4, there is a path-decomposition of G having at most p(G) 2 + ⌊( g+1 2g ) q(G) ⌋ paths, where p(G) is the number of vertices of odd degree in G and q(G) is the number of non-isolated vertices of even degree in G.
منابع مشابه
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A path (resp. cycle) decomposition of a graph G is a set of edge-disjoint paths (resp. cycles) of G that covers the edge set of G. Gallai (1966) conjectured that every graph on n vertices admits a path decomposition of size at most ⌊(n+ 1)/2⌋, and Hajós (1968) conjectured that every Eulerian graph on n vertices admits a cycle decomposition of size at most ⌊(n−1)/2⌋. Gallai’s Conjecture was veri...
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عنوان ژورنال:
- Journal of Graph Theory
دوره 75 شماره
صفحات -
تاریخ انتشار 2014