Minimum Genus and Maximum Genus

2013 ◽  
pp. 745-759
Author(s):  
Jianer Chen
Keyword(s):  
Maximum Genus

The Maximum Genus on a 3-Vertex-Connected Graph

2000 ◽  
Vol 16 (2) ◽  
pp. 159-164 ◽  
Author(s):  
Yuangqiu Huang
Keyword(s):  
Connected Graph ◽  
Maximum Genus

scholarly journals Maximum genus embeddings of Steiner triple systems

2005 ◽  
Vol 26 (3-4) ◽  
pp. 401-416 ◽  
Author(s):  
Mike J. Grannell ◽  
Terry S. Griggs ◽  
Jozef Širáň
Keyword(s):  
Steiner Triple Systems ◽  
Maximum Genus ◽  
Triple Systems

scholarly journals Matchings, Cycle Bases, and the Maximum Genus of a Graph

10.37236/2479 ◽  
2012 ◽  
Vol 19 (3) ◽  
Author(s):  
Michal Kotrbčík ◽  
Martin Škoviera
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Perfect Matching ◽  
Intersection Graph ◽  
Matching Number ◽  
Maximum Genus ◽  
Cycle Space ◽  
Intersection Graphs ◽  
Connected Graphs ◽  
Cycle Bases

We study the interplay between the maximum genus of a graph and bases of its cycle space via the corresponding intersection graph. Our main results show that the matching number of the intersection graph is independent of the basis precisely when the graph is upper-embeddable, and completely describe the range of matching numbers when the graph is not upper-embeddable. Particular attention is paid to cycle bases consisting of fundamental cycles with respect to a given spanning tree. For $4$-edge-connected graphs, the intersection graph with respect to any spanning tree (and, in fact, with respect to any basis) has either a perfect matching or a matching missing exactly one vertex. We show that if a graph is not $4$-edge-connected, different spanning trees may lead to intersection graphs with different matching numbers. We also show that there exist $2$-edge connected graphs for which the set of values of matching numbers of their intersection graphs contains arbitrarily large gaps.

scholarly journals Lower Bounds for the Average Genus of a CF-graph

10.37236/422 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Yichao Chen
Keyword(s):  
Lower Bound ◽  
Linear Function ◽  
Lower Bounds ◽  
Betti Number ◽  
Maximum Genus ◽  
Simple Graphs ◽  
Structure Theorems ◽  
Average Genus

CF-graphs form a class of multigraphs that contains all simple graphs. We prove a lower bound for the average genus of a CF-graph which is a linear function of its Betti number. A lower bound for average genus in terms of the maximum genus and some structure theorems for graphs with a given average genus are also provided.

The Maximum Genus of Cartesian Products of Graphs

1974 ◽  
Vol 26 (5) ◽  
pp. 1025-1035 ◽  
Author(s):  
Joseph Zaks
Keyword(s):  
Connected Graph ◽  
Connected Components ◽  
Open Disk ◽  
Maximum Genus ◽  
Cartesian Products ◽  
Euler’S Formula ◽  
Cartesian Products Of Graphs

The maximum genus γM(G) of a connected graph G has been defined in [2] as the maximum g for which there exists an embedding h : G —> S(g), where S(g) is a compact orientable 2-manifold of genus g, such that each one of the connected components of S(g) — h(G) is homeomorphic to an open disk; such an embedding is called cellular. If G is cellularly embedded in S(g), having V vertices, E edges and F faces, then by Euler's formulaV-E + F = 2-2g.

scholarly journals Maximum genus and chromatic number of graphs

2003 ◽  
Vol 271 (1-3) ◽  
pp. 117-127 ◽  
Author(s):  
Yuanqiu Huang
Keyword(s):  
Chromatic Number ◽  
Maximum Genus

Survey of results on the maximum genus of a graph

1979 ◽  
Vol 3 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Richard D. Ringeisen
Keyword(s):  
Maximum Genus

scholarly journals Finding a maximum-genus graph imbedding

1988 ◽  
Vol 35 (3) ◽  
pp. 523-534 ◽  
Author(s):  
Merrick L. Furst ◽  
Jonathan L. Gross ◽  
Lyle A. McGeoch
Keyword(s):  
Maximum Genus
Sign in / Sign up

Export Citation Format

Share Document