TY - JOUR

T1 - On a list (k, l)-coloring of incidentors in multigraphs of even degree for some values of k and l

AU - Pyatkin, Artem Valer evich

PY - 2019/5/20

Y1 - 2019/5/20

N2 - The problem of a list (k, l)-coloring of incidentors of a directed multigraph without loops is studied in the case where the lists of admissible colors for incidentors of each arc are integer intervals. According to a known conjecture, if the lengths of these interval are at least 2Δ + 2k - l - 1 for every arc, where Δ is the maximum degree of the multigraph, then there exists a list (k, l)-coloring of incidentors. We prove this conjecture for multigraphs of even maximum degree Δ with the following parameters: •l ≥ k + Δ/2; •l < k + Δ/2 and k or l is odd; • l < k + Δ/2 and k = 0 or l - k = 2.

AB - The problem of a list (k, l)-coloring of incidentors of a directed multigraph without loops is studied in the case where the lists of admissible colors for incidentors of each arc are integer intervals. According to a known conjecture, if the lengths of these interval are at least 2Δ + 2k - l - 1 for every arc, where Δ is the maximum degree of the multigraph, then there exists a list (k, l)-coloring of incidentors. We prove this conjecture for multigraphs of even maximum degree Δ with the following parameters: •l ≥ k + Δ/2; •l < k + Δ/2 and k or l is odd; • l < k + Δ/2 and k = 0 or l - k = 2.

KW - (K, L)-coloring

KW - Incidentors

KW - List coloring

KW - incidentors

KW - (k, l)-coloring

KW - list coloring

UR - http://www.scopus.com/inward/record.url?scp=85078439577&partnerID=8YFLogxK

U2 - 10.21538/0134-4889-2019-25-2-177-184

DO - 10.21538/0134-4889-2019-25-2-177-184

M3 - Article

AN - SCOPUS:85078439577

VL - 25

SP - 177

EP - 184

JO - Trudy Instituta Matematiki i Mekhaniki UrO RAN

JF - Trudy Instituta Matematiki i Mekhaniki UrO RAN

SN - 0134-4889

IS - 2

ER -