TY  - JOUR
ID  - Kozerenko2021
LB  - Kozerenko2021
AU  - Kozerenko, Sergiy
TI  - More on linear and metric tree maps
ST  - More on linear and metric tree maps
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2021
VL  - 41
IS  - 1
SP  - 55
EP  - 70
DO  - https://doi.org/10.7494/OpMath.2021.41.1.55
UR  - https://doi.org/10.7494/OpMath.2021.41.1.55
AB  - We consider linear and metric self-maps on vertex sets of finite combinatorial trees. Linear maps are maps which preserve intervals between pairs of vertices whereas metric maps are maps which do not increase distances between pairs of vertices. We obtain criteria for a given linear or a metric map to be a positive (negative) under some orientation of the edges in a tree, we characterize trees which admit maps with Markov graphs being paths and prove that the converse of any partial functional digraph is isomorphic to a Markov graph for some suitable map on a tree.
KW  - tree
KW  - Markov graph
KW  - metric map
KW  - non-expanding map
KW  - linear map
KW  - graph homomorphism
SN  - 1232-9274
ER  -