Gallai's conjecture asserts that every connected graph on n vertices can be decomposed into at most n+1/2 paths.The E-subgraph of a graph G,denoted by G_(e),is the subgraph induced by the vertices of even degree i...Gallai's conjecture asserts that every connected graph on n vertices can be decomposed into at most n+1/2 paths.The E-subgraph of a graph G,denoted by G_(e),is the subgraph induced by the vertices of even degree in G.A triangle pair is a graph consisting of two triangles with exactly one vertex in common.In this paper,it is proved that Gallai's conjecture is true for graphs G in which G_(e)contains no triangle pair and each block of G_(e)has maximum degree at most 3.展开更多
There are six types of triangles： undirected triangle, cyclic triangle, transitive triangle, mixed-1 triangle, mixed-2 triangle and mixed-3 triangle. The triangle-decompositions for the six types of triangles have al...There are six types of triangles： undirected triangle, cyclic triangle, transitive triangle, mixed-1 triangle, mixed-2 triangle and mixed-3 triangle. The triangle-decompositions for the six types of triangles have already been solved. For the first three types of triangles, their large sets have already been solved, and their overlarge sets have been investigated. In this paper, we establish the spectrum of LTi（v,λ）, OLTi（v）（i = 1, 2）, and give the existence of LT3（v, λ） and OLT3（v, λ） with λ even.展开更多
基金the National Natural Science Foundation of China(No.11971110).
文摘Gallai's conjecture asserts that every connected graph on n vertices can be decomposed into at most n+1/2 paths.The E-subgraph of a graph G,denoted by G_(e),is the subgraph induced by the vertices of even degree in G.A triangle pair is a graph consisting of two triangles with exactly one vertex in common.In this paper,it is proved that Gallai's conjecture is true for graphs G in which G_(e)contains no triangle pair and each block of G_(e)has maximum degree at most 3.
基金Supported by the National Natural Science Foundation of China(No.10371031) Doctor fund of Hebei Normal University
文摘There are six types of triangles： undirected triangle, cyclic triangle, transitive triangle, mixed-1 triangle, mixed-2 triangle and mixed-3 triangle. The triangle-decompositions for the six types of triangles have already been solved. For the first three types of triangles, their large sets have already been solved, and their overlarge sets have been investigated. In this paper, we establish the spectrum of LTi（v,λ）, OLTi（v）（i = 1, 2）, and give the existence of LT3（v, λ） and OLT3（v, λ） with λ even.
