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r - Creating new column combining info in two columns, alphabetically

I have a dataset of football teams that looks like this:

Home_team Away_team Home_score Away_score
Arsenal    Chelsea      1        3
Manchester U  Blackburn 2        9
Liverpool      Leeds    0        8
Chelsea     Arsenal     4        1

I want to group the teams involved, regardless of which teams were playing at home and away from home. For example, if Chelsea played Arsenal, regardless of whether the game was at Chelsea or at Arsenal, I would want the new column, "teams_involved", to be Arsenal - Chelsea. My guess is the way to do this is to add these teams to the new column in alphabetical order, but I'm not sure how to do that.

Desired output:

Home_team Away_team Home_score Away_score teams_involved
Arsenal    Chelsea      1        3     Arsenal - Chelsea
Manchester U  Blackburn 2        9   Blackburn - Manchester U
Liverpool      Leeds    0        8      Leeds - Liverpool 
Chelsea     Arsenal     4        1     Arsenal - Chelsea

The reason I am seeking this is so I can see the # of wins for each team against a specific team, regardless of the location of the game.

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df = read.table(text = "
Home_team Away_team Home_score Away_score
Arsenal    Chelsea      1        3
ManchesterU  Blackburn 2        9
Liverpool      Leeds    0        8
Chelsea     Arsenal     4        1
", header=T, stringsAsFactors=F)

library(dplyr)

df %>%
  rowwise() %>%      # for each row
  mutate(Teams = paste(sort(c(Home_team, Away_team)), collapse = " - ")) %>%  # sort the teams alphabetically and then combine them separating with -
  ungroup()          # forget the row grouping

# # A tibble: 4 x 5
#   Home_team   Away_team Home_score Away_score Teams                  
#   <chr>       <chr>          <int>      <int> <chr>                  
# 1 Arsenal     Chelsea            1          3 Arsenal - Chelsea      
# 2 ManchesterU Blackburn          2          9 Blackburn - ManchesterU
# 3 Liverpool   Leeds              0          8 Leeds - Liverpool      
# 4 Chelsea     Arsenal            4          1 Arsenal - Chelsea 

An alternative solution without rowwise:

# create function and vectorize it
f = function(x,y) {paste(sort(c(x, y)), collapse = " - ")}
f = Vectorize(f)

# apply function to your dataset
df %>% mutate(Teams = f(Home_team, Away_team))

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