Spanning k-trees of bipartite graphs

5Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

Abstract

A tree is called a k-tree if its maximum degree is at most k. We prove the following theorem. Let k ≥ 2 be an integer, and G be a connected bipartite graph with bipartition (A,B) such that |A| ≤ |B| ≤ (k−1)|A| + 1. If σk(G) ≥ |B|, then G has a spanning k-tree, where σk(G) denotes the minimum degree sum of k independent vertices of G. Moreover, the condition on σk(G) is sharp. It was shown by Win (Abh. Math. Sem. Univ. Hamburg, 43, 263–267, 1975) that if a connected graph H satisfies σk(H) ≥ |H|−1, then H has a spanning k-tree. Thus our theorem shows that the condition becomes much weaker if the graph is bipartite.

Author supplied keywords

References Powered by Scopus

On Hamiltonian bipartite graphs

129Citations
N/AReaders
Get full text

Spanning Trees: A Survey

97Citations
N/AReaders
Get full text

Spanning trees with bounded degrees

42Citations
N/AReaders
Get full text

Cited by Powered by Scopus

Plane Bichromatic Trees of Low Degree

6Citations
N/AReaders
Get full text

Rainbow and Properly Colored Spanning Trees in Edge-Colored Bipartite Graphs

2Citations
N/AReaders
Get full text

Maximum properly colored trees in edge-colored graphs

1Citations
N/AReaders
Get full text

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Cite

CITATION STYLE

APA

Kano, M., Suzuki, K., Ozeki, K., Tsugaki, M., & Yamashita, T. (2015). Spanning k-trees of bipartite graphs. Electronic Journal of Combinatorics, 22(1). https://doi.org/10.37236/3628

Readers' Seniority

Tooltip

Professor / Associate Prof. 3

50%

Lecturer / Post doc 3

50%

Readers' Discipline

Tooltip

Mathematics 4

67%

Agricultural and Biological Sciences 1

17%

Computer Science 1

17%

Save time finding and organizing research with Mendeley

Sign up for free