![](/files/happy5.png)
Georgakopoulos, Agelos
End-Devouring Rays ★
Author(s): Georgakopoulos
Problem Let
be a graph,
a countable end of
, and
an infinite set of pairwise disjoint
-rays in
. Prove that there is a set
of pairwise disjoint
-rays that devours
such that the set of starting vertices of rays in
equals the set of starting vertices of rays in
.
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ \omega $](/files/tex/80a4fb3738c5ceba7fa826deb56874dcbfc305a8.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ K $](/files/tex/fe461893b9f87593e8b79d83455b531cd9f29913.png)
![$ \omega $](/files/tex/80a4fb3738c5ceba7fa826deb56874dcbfc305a8.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ K' $](/files/tex/68b4ae741aca7464eb90767e39734ba565d96852.png)
![$ \omega $](/files/tex/80a4fb3738c5ceba7fa826deb56874dcbfc305a8.png)
![$ \omega $](/files/tex/80a4fb3738c5ceba7fa826deb56874dcbfc305a8.png)
![$ K' $](/files/tex/68b4ae741aca7464eb90767e39734ba565d96852.png)
![$ K $](/files/tex/fe461893b9f87593e8b79d83455b531cd9f29913.png)
Geodesic cycles and Tutte's Theorem ★★
Author(s): Georgakopoulos; Sprüssel
Problem If
is a
-connected finite graph, is there an assignment of lengths
to the edges of
, such that every
-geodesic cycle is peripheral?
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ 3 $](/files/tex/4aaf85facb6534fd470edd32dbdb4e28f6218190.png)
![$ \ell: E(G) \to \mathb R^+ $](/files/tex/aad2d29bf9a23e904e02b7e5f616c403cb1b95df.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ \ell $](/files/tex/d2c5960dd9795a1b000a5843d282c97268e303c4.png)
Keywords: cycle space; geodesic cycles; peripheral cycles
Hamiltonian cycles in powers of infinite graphs ★★
Author(s): Georgakopoulos
Conjecture
- \item If
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
Keywords: hamiltonian; infinite graph
Hamiltonian cycles in line graphs of infinite graphs ★★
Author(s): Georgakopoulos
Conjecture
- \item If
![$ 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
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