Abstract
A graph is called a weighted graph when each edge e is assigned a nonnegative number w(e), called the weight of e. For a vertex v of a weighted graph, d w (v) is the sum of the weights of the edges incident with v. For a subgraph H of a weighted graph G, the weight of H is the sum of the weights of the edges belonging to H. In this paper, we give a new sufficient condition for a weighted graph to have a heavy cycle. A 2-connected weighted graph G contains either a Hamilton cycle or a cycle of weight at least c, if G satisfies the following conditions: In every induced claw or induced modified claw F of G, (1) max{d w (x),d w (y)}≤ c/2 for each non-adjacent pair of vertices x and y in F, and (2) all edges of F have the same weight.
| Original language | English |
|---|---|
| Pages (from-to) | 217-229 |
| Number of pages | 13 |
| Journal | Graphs and Combinatorics |
| Volume | 21 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2005 Jun |
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Keywords
- Claw
- Fan-type condition
- Heavy cycle
- Modified claw
- Weighted graph
ASJC Scopus subject areas
- Mathematics(all)
- Discrete Mathematics and Combinatorics
Cite this
Claw conditions for heavy cycles in weighted graphs. / Fujisawa, Jun.
In: Graphs and Combinatorics, Vol. 21, No. 2, 06.2005, p. 217-229.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Claw conditions for heavy cycles in weighted graphs
AU - Fujisawa, Jun
PY - 2005/6
Y1 - 2005/6
N2 - A graph is called a weighted graph when each edge e is assigned a nonnegative number w(e), called the weight of e. For a vertex v of a weighted graph, d w (v) is the sum of the weights of the edges incident with v. For a subgraph H of a weighted graph G, the weight of H is the sum of the weights of the edges belonging to H. In this paper, we give a new sufficient condition for a weighted graph to have a heavy cycle. A 2-connected weighted graph G contains either a Hamilton cycle or a cycle of weight at least c, if G satisfies the following conditions: In every induced claw or induced modified claw F of G, (1) max{d w (x),d w (y)}≤ c/2 for each non-adjacent pair of vertices x and y in F, and (2) all edges of F have the same weight.
AB - A graph is called a weighted graph when each edge e is assigned a nonnegative number w(e), called the weight of e. For a vertex v of a weighted graph, d w (v) is the sum of the weights of the edges incident with v. For a subgraph H of a weighted graph G, the weight of H is the sum of the weights of the edges belonging to H. In this paper, we give a new sufficient condition for a weighted graph to have a heavy cycle. A 2-connected weighted graph G contains either a Hamilton cycle or a cycle of weight at least c, if G satisfies the following conditions: In every induced claw or induced modified claw F of G, (1) max{d w (x),d w (y)}≤ c/2 for each non-adjacent pair of vertices x and y in F, and (2) all edges of F have the same weight.
KW - Claw
KW - Fan-type condition
KW - Heavy cycle
KW - Modified claw
KW - Weighted graph
UR - http://www.scopus.com/inward/record.url?scp=21544444165&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=21544444165&partnerID=8YFLogxK
U2 - 10.1007/s00373-005-0607-2
DO - 10.1007/s00373-005-0607-2
M3 - Article
AN - SCOPUS:21544444165
VL - 21
SP - 217
EP - 229
JO - Graphs and Combinatorics
JF - Graphs and Combinatorics
SN - 0911-0119
IS - 2
ER -