Circular chromatic index of type 1 Blanuša snarks

We develop a general model of edge spaces in order to generalize, unify, and simplify previous work on cycle spaces of infinite graphs. We give simple topological criteria to show that the fundamental cycles of a (generalization of a) spanning tree generate the cycle space in a connected, compact, weakly Hausdorff edge space. Furthermore, in such a space, the orthogonal complement of the bond space is the cycle space. This work unifies the two different notions of cycle space as introduced by Diestel and Kuhn [Combinatorica 24 (2004), 68–89 and Eur J Combin 25 (2004), 835–862] and by Bonnington and Richter [J Graph Theory 44 (2003), 132–147]. © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 115–144, 2008

[1]  Henning Bruhn,et al.  The cycle space of a 3-connected locally finite graph is generated by its finite and infinite peripheral circuits , 2004, J. Comb. Theory, Ser. B.

[2]  Reinhard Diestel,et al.  On Infinite Cycles I , 2004, Comb..

[3]  Karel Casteels.  The Cycle Spaces of an Infinite Graph , 2006 .

[4]  Reinhard Diestel,et al.  End spaces and spanning trees , 2006, J. Comb. Theory, Ser. B.

[5]  Reinhard Diestel,et al.  The Cycle Space of an Infinite Graph , 2005, Combinatorics, Probability and Computing.

[6]  Reinhard Diestel,et al.  Graph Theory , 1997 .

[7]  Reinhard Diestel,et al.  Graph-theoretical versus topological ends of graphs , 2003, J. Comb. Theory, Ser. B.

[8]  W. Voxman,et al.  Aspects of Topology , 1998 .

[9]  K. Hofmann.  d-1 – The Low Separation Axioms T0 and T1 , 2003 .

[10]  J. Nikiel,et al.  Continuous Images of Arcs and Inverse Limit Methods , 1993 .

[11]  C. Paul Bonnington,et al.  Graphs embedded in the plane with a bounded number of accumulation points , 2003 .

[12]  CARSTEN THOMASSEN,et al.  Graph-like continua, augmenting arcs, and Menger’s theorem , 2008, Comb..

[13]  Philipp Sprüssel.  End spaces of graphs are normal , 2008, J. Comb. Theory, Ser. B.

[14]  Reinhard Diestel,et al.  Topological paths, cycles and spanning trees in infinite graphs , 2004, Eur. J. Comb..

[15]  Lynn Arthur Steen,et al.  Counterexamples in Topology , 1970 .

[16]  Antoine Vella,et al.  A Fundamentally Topological Perspective on Graph Theory , 2005 .