![](/files/happy5.png)
infinite graph
Characterizing (aleph_0,aleph_1)-graphs ★★★
Call a graph an -graph if it has a bipartition
so that every vertex in
has degree
and every vertex in
has degree
.
![$ (\aleph_0,\aleph_1) $](/files/tex/4170402299493c216234845dcc59a455da96e488.png)
Keywords: binary tree; infinite graph; normal spanning tree; set theory
Highly arc transitive two ended digraphs ★★
Author(s): Cameron; Praeger; Wormald
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
Keywords: arc transitive; digraph; infinite graph
Strong matchings and covers ★★★
Author(s): Aharoni
Let be a hypergraph. A strongly maximal matching is a matching
so that
for every matching
. A strongly minimal cover is a (vertex) cover
so that
for every cover
.
![$ H $](/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png)
![$ \le k $](/files/tex/26d614fff037e5976f481eab5b4e36c487e120ac.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ H $](/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png)
Keywords: cover; infinite graph; matching
Unfriendly partitions ★★★
If is a graph, we say that a partition of
is unfriendly if every vertex has at least as many neighbors in the other classes as in its own.
Keywords: coloring; infinite graph; partition
Hamiltonian cycles in powers of infinite graphs ★★
Author(s): Georgakopoulos
- \item If
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
Keywords: hamiltonian; infinite graph
Hamiltonian cycles in line graphs of infinite graphs ★★
Author(s): Georgakopoulos
- \item If
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ L(G) $](/files/tex/76f6ee75811ed6d89f7e99f8aa7a505f462c30b2.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ L(G) $](/files/tex/76f6ee75811ed6d89f7e99f8aa7a505f462c30b2.png)
Keywords: hamiltonian; infinite graph; line graphs
Infinite uniquely hamiltonian graphs ★★
Author(s): Mohar
![$ r > 2 $](/files/tex/97a6c1471f5d46c5d21bf3e382139df59f21bd80.png)
Keywords: hamiltonian; infinite graph; uniquely hamiltonian
Unions of triangle free graphs ★★★
![$ K_4 $](/files/tex/03778d11eadbb74fc862e7762ec7ce773f0b9413.png)
![$ \aleph_0 $](/files/tex/ae61eb32cc3c2cd0fc395f5f137af2ecebcc6f92.png)
Keywords: forbidden subgraph; infinite graph; triangle free
Seymour's self-minor conjecture ★★★
Author(s): Seymour
Keywords: infinite graph; minor
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