On path decompositions of 2k-regular graphs
نویسندگان
چکیده
منابع مشابه
On path decompositions of 2k-regular graphs
Tibor Gallai conjectured that the edge set of every connected graph G on n vertices can be partitioned into ⌈n/2⌉ paths. Let Gk be the class of all 2k-regular graphs of girth at least 2k − 2 that admit a pair of disjoint perfect matchings. In this work, we show that Gallai’s conjecture holds in Gk, for every k ≥ 3. Further, we prove that for every graph G in Gk on n vertices, there exists a par...
متن کاملPath decompositions of regular graphs with prescribed girth
A P -decomposition of a graph G is a set of pairwise edge-disjoint paths of G with edges that cover the edge set of G. Kotzig (1957) proved that a 3-regular graph admits a P3-decomposition if and only if it contains a perfect matching, and also asked what are the necessary and sufficient conditions for an -regular graph to admit a P -decomposition, for odd . Let g, and m be positive integers wi...
متن کاملA result on decompositions of regular graphs
Su, X.-Y., A result on decompositions of regular graphs, Discrete Mathematics 105 (1992) 323-326. We prove that for any connected graph G and any integer r which is a common multiple of the degrees of the vertices in G, there exists a connected, r-regular, and G-decomposable graph H such that x(H) = x(G) and o(H) = w(G), where x and w are the chromatic number and the clique number, respectively...
متن کاملPath Algorithms on Regular Graphs
We consider standard algorithms of finite graph theory, like for instance shortest path algorithms. We present two general methods to polynomially extend these algorithms to infinite graphs generated by deterministic graph grammars.
متن کاملCompatible circuit decompositions of 4-regular graphs
A transition system T of an Eulerian graph G is a family of partitions of the edges incident to each vertex of G into transitions i.e. subsets of size two. A circuit decomposition C of G is compatible with T if no pair of adjacent edges of G is both a transition of T and consecutive in a circuit of C. We give a conjectured characterization of when a 4-regular graph has a transition system which...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2017
ISSN: 0012-365X
DOI: 10.1016/j.disc.2016.09.029