Name
Abstract | ||
|---|---|---|
AbstractLet $$G$$G be a graph and $$f:V(G)\rightarrow \{1,2,3,4,\ldots \}$$f:V(G) {1,2,3,4, } be a function. We denote by $$odd(G)$$odd(G) the number of odd components of $$G$$G. We prove that if $$odd(G-X)\le \sum _{x\in X}f(x)$$odd(G-X)≤ x Xf(x) for all $$ X\subset V(G)$$X V(G), then $$G$$G has a $$(1,f)$$(1,f)-factor $$F$$F such that, for every vertex $$v$$v of $$G$$G, if $$f(v)$$f(v) is even, then $$\deg _F(v)\in \{1,3,\ldots ,f(v)-1,f(v)\}$$degF(v) {1,3, ,f(v)-1,f(v)}, and otherwise $$\deg _F(v)\in \{1,3, \ldots , f(v)\}$$degF(v) {1,3, ,f(v)}. This theorem is a generalization of both the $$(1,f)$$(1,f)-odd factor theorem and a recent result on $$\{1,3, \ldots , 2n-1,2n\}$${1,3, ,2n-1,2n}-factors by Lu and Wang. We actually prove a result stronger than the above theorem. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/s00373-015-1558-x | Periodicals |
Keywords | Field | DocType |
Factor of graph,(1, f)-Odd factor,Odd components | Graph,Factor theorem,Combinatorics,Vertex (geometry),Mathematics | Journal |
Volume | Issue | ISSN |
32 | 1 | 0911-0119 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yoshimi Egawa | 1 | 24 | 10.00 |
| Mikio Kano | 2 | 548 | 99.79 |
| Zheng Yan | 3 | 0 | 2.37 |